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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #18 : X And Y Intercept

Find the x-intercept(s) for the circle defined by (x+1)^2 + (y-3)^2 = 25

Possible Answers:

x = 3

x = 7

x= 5, -3

x = 5

x=3, -5

Correct answer:

x=3, -5

Explanation:

The x-intercepts occur when y is equal to zero. So to figure out the x-intercepts, plug in 0 for y:

(x+1)^2 + (0-3)^2 = 25

(x+1)^2 + 9 = 25 subtract 9 from both sides

(x+1)^2 = 16 take the square root of both sides

x + 1 = 4, -4 there are 2 possibilities here since 4^2 = 16 and also (-4)^2 = 16

One solution: x + 1 = 4 subtract 1 from both sides

x = 3

The other solution: x + 1 = -4 subtract 1 from both sides

x = -5

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Example Question #241 : Coordinate Geometry

Find the y-intercept(s) for the equation y = |x - 3|

Possible Answers:

y = 3, -3

y = 3, 6

y = 0, 6

y = -3

y = 3

Correct answer:

y = 3

Explanation:

The y-intercept occurs when x is 0, so plug in 0 for x:

y = | 0 - 3| = | -3| = 3

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Example Question #20 : X And Y Intercept

Find the x- and y-intercepts for the equation y =-2x+ 5

Possible Answers:

(2.5, 0); (0,5)

(10, 0 ) ; (5, 0 )

(10, 0 ) ; (0 , -5)

(-2.5, 0 ) ; (0, 5)

(0, 2.5); (5, 0 )

Correct answer:

(2.5, 0); (0,5)

Explanation:

To find the x-intercept, plug in 0 for y:

0 = -2x+ 5 subtract 5 from both sides

-5 = -2x divide both sides by -2

2.5 = x since x is 2.5 and y is 0, this point is (2.5, 0 )

To find the y-intercept, plug in 0 for x:

y = -2(0)+ 5

y = 0 + 5 = 5

This gives the point (0,5)

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Example Question #21 : How To Find X Or Y Intercept

Find the -intercept for the line 2x-y=12 .

Possible Answers:

(6, 0)

(-6, 0)

(0, 6)

(0, -6)

Correct answer:

(6, 0)

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

2x-y=12

y+12=2x

y=2x-12

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

2x-12=0

Now, solve for .

2x=12

x=6

The x-intercept is found at (6, 0) .

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Example Question #1522 : Intermediate Geometry

Find the x-intercept for the line 12x-9y=4 .

Possible Answers:

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

$(\frac{4}{3}, 0)$

$(\frac{1}{3}, 0)$

$(-\frac{1}{3},0)$

Correct answer:

$(\frac{1}{3}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

12x-9y=4

9y+4=12x

9y=12x-4

$y=\frac{4}{3}x-\frac{4}{9}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{4}{3}x-\frac{4}{9}$

Now, solve for .

$\frac{4}{3}x=\frac{4}9$

$x=\frac{1}{3}$

The x-intercept is found at $(\frac{1}{3}, 0)$ .

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Example Question #21 : How To Find X Or Y Intercept

Find the x-intercept for the line 12x-2y=2 .

Possible Answers:

(6, 0)

$(\frac{1}{6}, 0)$

$(-\frac{2}{3}, x)$

$(\frac{1}{3}, 0)$

Correct answer:

$(\frac{1}{6}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

12x-2y=2

2y+2=12x

2y=12x-2

y=6x-1

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

0=6x-1

Now, solve for .

6x=1

$x=\frac{1}{6}$

The x-intercept is found at $(\frac{1}{6}, 0)$ .

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Example Question #22 : How To Find X Or Y Intercept

Find the x-intercept for the line 10y-5x=25 .

Possible Answers:

(-5, 0)

$(-\frac{5}{2}, 0)$

$(\frac{3}{5}, 0)$

$(\frac{1}{5}, 0)$

Correct answer:

(-5, 0)

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

10y-5x=25

10y=5x+25

$y=\frac{1}{2}x+\frac{5}{2}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{1}{2}x+\frac{5}{2}$

Now, solve for .

$\frac{1}{2}x=-\frac{5}{2}$

x=-5

The x-intercept is found at (-5, 0) .

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Example Question #22 : How To Find X Or Y Intercept

Find the x-intercept for the line 5x-2y=4 .

Possible Answers:

$(-\frac{5}{4}, 0)$

$(\frac{3}{5}, 0)$

$(\frac{5}{2}, 0)$

$(\frac{4}{5}, 0)$

Correct answer:

$(\frac{4}{5}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

5x-2y=4

2y+4=5x

2y=5x-4

$y=\frac{5}{2}x-2$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{5}{2}x-2$

Now, solve for .

$\frac{5}{2}x=2$

$x=\frac{4}{5}$

The x-intercept is found at $(\frac{4}{5}, 0)$ .

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Example Question #24 : How To Find X Or Y Intercept

Find the x-intercept of the line 3y-6x=21 .

Possible Answers:

$(\frac{3}{7}, 0)$

$(-\frac{7}{2}, 0)$

$(\frac{5}{2}, 0)$

(-4, 0)

Correct answer:

$(-\frac{7}{2}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

3y-6x=21

3y=6x+21

y=2x+7

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

0=2x+7

Now, solve for .

2x=-7

$x=-\frac{7}{2}$

The x-intercept is found at $(-\frac{7}{2}, 0)$ .

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Example Question #25 : How To Find X Or Y Intercept

Find the x-intercept of the line 12x-15y=-6 .

Possible Answers:

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

$(-\frac{1}{2},0)$

(-3, 0)

(-2, 0)

Correct answer:

$(-\frac{1}{2},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

12x-15y=-6

15y-6=12x

15y=12x+6

$y=\frac{4}{5}x+\frac{2}{5}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{4}{5}x+\frac{2}{5}$

Now, solve for .

$\frac{4}{5}x=-\frac{2}{5}$

$x=-\frac{1}{2}$

The x-intercept is found at $(-\frac{1}{2}, 0)$ .

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #18 : X And Y Intercept

Example Question #241 : Coordinate Geometry

Example Question #20 : X And Y Intercept

Example Question #21 : How To Find X Or Y Intercept

Example Question #1522 : Intermediate Geometry

Example Question #21 : How To Find X Or Y Intercept

Example Question #22 : How To Find X Or Y Intercept

Example Question #22 : How To Find X Or Y Intercept

Example Question #24 : How To Find X Or Y Intercept

Example Question #25 : How To Find X Or Y Intercept

All Intermediate Geometry Resources

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