# 4gmat diagnostic test q14 - problem solving - coordinate geometry

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1. GMAT QUANTITATIVE REASONING COORDINATE GEOMETRY PROBLEM SOLVING Diagnostic Test 2. Question What is the area of the triangle formed by the coordinate axes and the line L whose equation is 2x - 3y = 6? A. 6 B. 12 C. 13 D. 3 E. 7.5 3. Step 1 What kind of a triangle is formed? 4. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 5. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 The coordinate axes (x and y axes) form sides of the triangle. The triangle is a right triangle. 6. Step 2 Plot the line on the x-y plane; determine sides of the triangle; compute area 7. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Steps to compute area of the triangle 8. Compute x and y intercepts using the equation of the line. x & y intercepts 01 What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Steps to compute area of the triangle 9. Compute x and y intercepts using the equation of the line. Determine sides of the triangle from x and y intercepts x & y intercepts Sides of triangle 01 02 What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Steps to compute area of the triangle 10. Compute x and y intercepts using the equation of the line. Determine sides of the triangle from x and y intercepts Using data on sides, compute area of triangle x & y intercepts Sides of triangle Find area 01 02 03 What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Steps to compute area of the triangle 11. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. Equation of the line is 2x 3y = 6 Step 01 : Compute x and y intercepts 12. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. Equation of the line is 2x 3y = 6 x-intercept is the point where the line meets the x-axis. At that point, the y coordinate is 0 (zero) Step 01 : Compute x and y intercepts 13. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. Equation of the line is 2x 3y = 6 x-intercept is the point where the line meets the x-axis. At that point, the y coordinate is 0 (zero) Step 01 : Compute x and y intercepts To determine x-intercept of a line, substitute y = 0 in the equation of the line. 14. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. Equation of the line is 2x 3y = 6 x-intercept is the point where the line meets the x-axis. At that point, the y coordinate is 0 (zero) Step 01 : Compute x and y intercepts To determine x-intercept of a line, substitute y = 0 in the equation of the line. 2x 3(0) = 6 or x = 3. x-intercept of the line is 3 15. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. Equation of the line is 2x 3y = 6 x-intercept is the point where the line meets the x-axis. At that point, the y coordinate is 0 (zero) Step 01 : Compute x and y intercepts To determine x-intercept of a line, substitute y = 0 in the equation of the line. 2x 3(0) = 6 or x = 3. x-intercept of the line is 3 y-intercept is the point where the line meets the y-axis. At that point, the x coordinate is 0 (zero) 16. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. Equation of the line is 2x 3y = 6 x-intercept is the point where the line meets the x-axis. At that point, the y coordinate is 0 (zero) Step 01 : Compute x and y intercepts To determine x-intercept of a line, substitute y = 0 in the equation of the line. 2x 3(0) = 6 or x = 3. x-intercept of the line is 3 y-intercept is the point where the line meets the y-axis. At that point, the x coordinate is 0 (zero) To determine y-intercept of a line, substitute x = 0 in the equation of the line. 17. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. Equation of the line is 2x 3y = 6 x-intercept is the point where the line meets the x-axis. At that point, the y coordinate is 0 (zero) Step 01 : Compute x and y intercepts To determine x-intercept of a line, substitute y = 0 in the equation of the line. 2x 3(0) = 6 or x = 3. x-intercept of the line is 3 y-intercept is the point where the line meets the y-axis. At that point, the x coordinate is 0 (zero) To determine y-intercept of a line, substitute x = 0 in the equation of the line. 2(0) 3y = 6 or y = -2. y-intercept of the line is -2 18. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle 19. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle Join the x and y intercepts to plot the line. 20. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) Join the x and y intercepts to plot the line. 21. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. 22. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. 23. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. OAB is the triangle whose area has to be determined. O A B 24. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. OAB is the triangle whose area has to be determined. O A B OA, one of the sides of the right triangle is the x intercept of the line = 3 units 25. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. OAB is the triangle whose area has to be determined. O A B OB, another side of the triangle is the y intercept of the line = 2 units OA, one of the sides of the right triangle is the x intercept of the line = 3 units 26. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. OAB is the triangle whose area has to be determined. O A B OB, another side of the triangle is the y intercept of the line = 2 units Step 03 : Compute the area OA, one of the sides of the right triangle is the x intercept of the line = 3 units 27. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. OAB is the triangle whose area has to be determined. O A B OB, another side of the triangle is the y intercept of the line = 2 units Step 03 : Compute the area Triangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units. OA, one of the sides of the right triangle is the x intercept of the line = 3 units 28. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. OAB is the triangle whose area has to be determined. O A B OB, another side of the triangle is the y intercept of the line = 2 units Step 03 : Compute the area Triangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units. Area = 1 2 b h = 1 2 3 2 = 3 units OA, one of the sides of the right triangle is the x intercept of the line = 3 units 29. What is the area of the triangle? Triangle is formed by the coordinate axes and the line 2x - 3y = 6 02 Compute area of the triangle. x intercept of line 3 and y intercept -2 Step 02 : Determine sides of triangle (3, 0) (0, -2) Join the x and y intercepts to plot the line. OAB is the triangle whose area has to be determined. O A B OB, another side of the triangle is the y intercept of the line = 2 units Step 03 : Compute the area Triangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units. Area = 1 2 b h = 1 2 3 2 = 3 units Choice D. OA, one of the sides of the right triangle

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