GMAT Math : Coordinate Geometry

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Example Questions

Example Question #701 : Geometry

What is the -intercept of a line that includes points (2,5) and (7,1) ?

Possible Answers:

$\left (0, 3\frac{2}{5} \right )$

$\left (0, 7\right )$

$\left (0, 6\frac{4}{5} \right )$

$\left (0, 6\frac{3}{5} \right )$

$\left (0, 7\frac{1}{5} \right )$

Correct answer:

$\left (0, 6\frac{3}{5} \right )$

Explanation:

The slope of the line is

$m = \frac{y _{2}- y _{1}}{x _{2}- x _{1}}=\frac{1- 5}{7- 2} = \frac{-4}{5} = - \frac{4}{5}$

Use the point slope form to find the equation of the line.

$y - y_{1} = m \left ( x - x_{1}\right )$

$y - 5= - \frac{4}{5} \left ( x - 2\right )$

Now substitute x=0 and solve for .

$y - 5= - \frac{4}{5} \left ( 0 - 2\right )$

$y - 5= \frac{8}{5}$

$y = \frac{8}{5} + 5 = \frac{8}{5} + \frac{25}{5} = \frac{33}{5} = 6\frac{3}{5}$

The -intercept is $\left (0, 6\frac{3}{5} \right )$

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Example Question #702 : Geometry

Give the area of the region on the coordinate plane bounded by the -axis, the -axis, and the graph of the equation 3x + 4y = 15 .

Possible Answers:

$18\frac{3}{4}$

$7\frac{1}{2}$

$9 \frac{3}{8}$

Correct answer:

$9 \frac{3}{8}$

Explanation:

This can best be solved using a diagram and noting the intercepts of the line of the equation 3x + 4y = 15 , which are calculated by substituting 0 for and separately and solving for the other variable.

-intercept:

3x + 4y = 15

$3x + 4 \cdot 0 = 15$

3x = 15

x = 5

-intercept:

3x + 4y = 15

$3 \cdot 0 + 4y = 15$

4y = 15

$y = 3 \frac{3}{4}$

Now, we can make and examine the diagram below - the red line is the graph of the equation 3x + 4y = 15 :

Triangle_2

The pink triangle is the one whose area we want; it is a right triangle whose legs, which can serve as base and height, are of length $5, 3\frac{3}{4}$ . We can compute its area:

$\frac{1}{2} \cdot 5 \cdot 3\frac{3}{4}= \frac{1}{2} \cdot \frac{5}{1} \cdot \frac{15}{4} = \frac{75}{8} = 9 \frac{3}{8}$

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Example Question #942 : Problem Solving Questions

What is the -intercept of 3x+2y=2

Possible Answers:

(3,0)

(2,0)

$(\frac{3}{2},0)$

$(\frac{2}{3},0)$

Correct answer:

$(\frac{2}{3},0)$

Explanation:

To solve for the -intercept, you have to set to zero and solve for :

3x+2y=2

3x+2(0)=2

3x=2

$x=\frac{2}{3}$

$(\frac{2}{3},0)$

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Example Question #702 : Geometry

What is -intercept for 3x+2y=2

Possible Answers:

(1,0)

$(0,\frac{2}{3})$

$(\frac{2}{3},0)$

(0,1)

Correct answer:

(0,1)

Explanation:

To solve for the -intercept, you have to set to zero and solve for :

3x+2y=2

3(0)+2y=2

2y=2

y=1

(0,1)

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Example Question #6 : X And Y Intercept

A line with slope $-\frac{4}{5}$ includes point (6,N) . What is the -intercept of this line in terms of ?

Possible Answers:

$\left (0, N+ \frac{24}{5} \right )$

$\left (0, N- \frac{24}{5} \right )$

$\left (0, \frac{4}{5}N+6 \right )$

$\left (0, \frac{4}{5}N-6 \right )$

$\left (0, \frac{4}{5}N-\frac{6}{5} \right )$

Correct answer:

$\left (0, N+ \frac{24}{5} \right )$

Explanation:

For some real number , the -intercept of the line will be some point (0,b) . We can set up the slope equation and solve for as follows:

$\frac{y_2-y_1}{x_2-x_1} = m$

$\frac{b-N}{0-6} =-\frac{4}{5}$

$\frac{b-N}{-6} =-\frac{4}{5}$

$\frac{b-N}{-6} \cdot (-6)=-\frac{4}{5}\cdot (-6)$

$b-N = \frac{24}{5}$

$b-N+N =N+ \frac{24}{5}$

$b =N+ \frac{24}{5}$

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Example Question #3 : Calculating X Or Y Intercept

Give the $y \;$ -intercept(s) of the graph of the equation

$y = 3x^{2} -2x - 16$

Possible Answers:

The graph has no $y\;$ -intercept.

$\left ( 0, \frac{8}{3}\right )$

(0,-2 )

(0,-16 )

(0,3 )

Correct answer:

(0,-16 )

Explanation:

Substitute 0 for :

$y = 3x^{2} -2x - 16$

$y = 3 \cdot 0^{2} -2 \cdot 0 - 16 = 0 - 0 -16 = -16$

The $y \;$ -intercept is (0,-16)

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Example Question #8 : X And Y Intercept

Give the -intercept(s) of the graph of the equation

$y = 3x^{2} -2x - 16$

Possible Answers:

$\left ( -8, 0 \right ), ( 2,0)$

$(-2,0), \left ( \frac{8}{3}, 0 \right )$

$(-2,0), \left ( 8, 0 \right )$

$\left (-16,0 \right )$

$\left ( -\frac{8}{3}, 0 \right ), ( 2,0)$

Correct answer:

$(-2,0), \left ( \frac{8}{3}, 0 \right )$

Explanation:

Set y = 0

$y = 3x^{2} -2x - 16$

$3x^{2} -2x - 16 = 0$

Using the -method, we look to split the middle term of the quadratic expression into two terms. We are looking for two integers whose sum is and whose product is $3 \left ( -16 \right ) = -48$ ; these numbers are -8,6 .

$3x^{2} -8x + 6x - 16 = 0$

$\left (3x^{2} -8x \right )+ \left ( 6x - 16 \right ) = 0$

$x \left (3x -8 \right )+ 2 \left (3 x - 8 \right ) = 0$

$\left ( x + 2 \right )\left (3x -8 \right ) = 0$

Set each linear binomial to 0 and solve:

x + 2 = 0

x + 2 - 2 = 0 - 2

x = -2

3x - 8 =0

3x - 8+ 8 =0 + 8

3x = 8

$3x\div 3 = 8 \div 3$

$x = \frac{8}{3}$

There are two -intercepts - $(-2,0), \left ( \frac{8}{3}, 0 \right )$

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Example Question #942 : Problem Solving Questions

A line includes (5,3) and (5,9) . Give its -intercept.

Possible Answers:

(0,6)

The line has no -intercept.

(0,5)

(0,12)

(0,-3 )

Correct answer:

The line has no -intercept.

Explanation:

The two points have the same coordinate, which is 5; the line is therefore vertical. This makes the line parallel to the -axis, meaning that it does not intersect it. Therefore, the line has no -intercept.

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Example Question #702 : Geometry

What are the and intercepts of the function $y= \ln(x+3)$ ?

Possible Answers:

y-intercept at (0,0)

x-intercept at (0,0)

y-intercept at (0,2)

x-intercept at (-3,2)

y-intercept at (-2, 0)

x-intercept at (0,3)

None of the other answers

Correct answer:

None of the other answers

Explanation:

The correct answer is

y-intercept at $(0,\ln(3))$

x-intercept at (-2,0)

To find the y-intercept, we plug in for and solve for

So we have $y = \ln(3+0) = \ln(3)$ . This is as simplified as we can get.

To find the x-intercept, we plug in for and solve for

So we have $0 = \ln(x+3)$

$e^0 = e^{\ln(x+3)}$ (Exponentiate both sides)

1 = x+3 ( e^0 is 1, and cancel the and ln on the right side)

x= -2

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Example Question #943 : Problem Solving Questions

Fill in the circle with a number so that the graph of the resulting equation has -intercept (0,5) :

$4 x+ \bigcirc y = 18$

Possible Answers:

$\frac{5}{4}$

$\frac{4}{5}$

$\frac{5}{18}$

$\frac{18 }{5}$

Correct answer:

$\frac{18 }{5}$

Explanation:

Let be the number in the circle. The equation can be written as

4 x+N y = 18

Substitute 0 for and 5 for ; the equation becomes

$4 \cdot 0+N \cdot 5 = 18$

0+5N = 18

5N = 18

$N = \frac{18 }{5}$

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GMAT Math : Coordinate Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #701 : Geometry

Example Question #702 : Geometry

Example Question #942 : Problem Solving Questions

Example Question #702 : Geometry

Example Question #6 : X And Y Intercept

Example Question #3 : Calculating X Or Y Intercept

Example Question #8 : X And Y Intercept

Example Question #942 : Problem Solving Questions

Example Question #702 : Geometry

Example Question #943 : Problem Solving Questions

All GMAT Math Resources

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