4gmat diagnostic test q14 - problem solving - coordinate geometry
TRANSCRIPT
GMAT QUANTITATIVE REASONING
COORDINATE GEOMETRY
PROBLEM SOLVING
Diagnostic Test
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
Step 1
What kind of a triangle is formed?
What is the area of the triangle?Triangle is formed by the coordinate axes and the line 2x - 3y = 6
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.
Step 2
Plot the line on the x-y plane; determine
sides of the triangle; compute area
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
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
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
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
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
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
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.
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
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)
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.
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
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
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 triangleJoin the x and y intercepts to plot the line.
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.
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.
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.
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
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
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
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
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 areaTriangle 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
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 areaTriangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units.
Area = 12× b × h =
12× 3 × 2 = 3 units
OA, one of the sides of the right triangle is the x intercept of the line = 3 units
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 areaTriangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units.
Area = 12× b × h =
12× 3 × 2 = 3 units Choice D.
OA, one of the sides of the right triangle is the x intercept of the line = 3 units
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