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HSPT Math : Geometry

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Example Questions

Example Question #1 : How To Find X Or Y Intercept

Give the -intercept, if there is one, of the graph of the equation

$y = \frac{1}{x^{2}+ x} + 3$

Possible Answers:

(0,3)

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

(0,4)

The graph has no -intercept.

(0,2)

Correct answer:

The graph has no -intercept.

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

$y = \frac{1}{x^{2}+ x} + 3$

$y = \frac{1}{0^{2}+0} + 3$

$y = \frac{1}{0} + 3$

However, since this expression has 0 in a denominator, it is of undefined value. This means that there is no value of paired with -coordinate 0, and, subsequently, the graph of the equation has no -intercept.

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Example Question #2 : How To Find X Or Y Intercept

Give the -intercept, if there is one, of the graph of the equation

$y = \frac{3}{\left | 3x-8\right |}$

Possible Answers:

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

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

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

The graph has no -intercept.

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

Correct answer:

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

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

$y = \frac{3}{\left | 3x-8\right |}$

$y = \frac{3}{\left | 3 \cdot 0 -8\right |}$

$y = \frac{3}{\left | 0 -8\right |}$

$y = \frac{3}{\left | -8\right |}$

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

The -intercept is $\left ( 0, \frac{3}{8}\right )$ .

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Example Question #3 : How To Find X Or Y Intercept

Give the -intercept, if there is one, of the graph of the equation

$y = 3(x-2)^{2} + 4 (x-7)$ .

Possible Answers:

(0, -16)

(0, -42)

The graph does not have a -intercept.

(0, -64)

(0, 8)

Correct answer:

(0, -16)

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

$y = 3(x-2)^{2} + 4 (x-7)$

$y = 3(0-2)^{2} + 4 (0-7)$

$y = 3( -2)^{2} + 4 ( -7)$

$y = 3 \cdot 4 + 4 ( -7)$

y = 12+ 4 ( -7)

y = 12+ (-28)

y = -16

The -intercept is the point (0, -16) .

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Example Question #1 : How To Find A Line On A Coordinate Plane

Give the slope of the line that passes through (5,3) and (-1, 5) .

Possible Answers:

$\frac{4}{3}$

$\frac{1}{3}$

$-\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

Use the slope formula, substituting $x_{1}= 5, y_{1}=3,x_{2}= -1, y_{2}=5$ :

$m =\frac{ y_{2}- y_{1} }{x_{2} - x_{1}}=\frac{ 5-3 }{-1-5} = \frac{ 2 }{-6} =-\frac{1 }{3}$

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Example Question #2081 : Hspt Mathematics

What is the slope of the line that passes through (4,4) and (8,8) ?

Possible Answers:

1.5

2.5

0.5

Correct answer:

Explanation:

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-4}{8-4}=\frac{4}{4}=1$

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Example Question #301 : Geometry

What is the slope of the line that passes through (4,7) and (-3,-7) ?

Possible Answers:

1.5

3.5

Correct answer:

Explanation:

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-7-7}{-3-4}=\frac{-14}{-7}=2$

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Example Question #302 : Geometry

What is the slope given the points (3,6) and (-4,5) ?

Possible Answers:

$\frac{1}{7}$

$-\frac{1}{7}$

Correct answer:

$\frac{1}{7}$

Explanation:

Write the slope equation, substitute the point values, and solve for the slope.

$m=\frac{y_2-y_1}{x_2-x_1}= \frac{5-6}{-4-3}= \frac{-1}{-7}= \frac{1}{7}$

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Example Question #2082 : Hspt Mathematics

A point (2,-4) is shifted $\textup{3 units}$ to the left and $\textup{5 units}$ down. What is the new point?

Possible Answers:

(-1,-9)

(5,9)

(3,5)

(1,-9)

(-1,1)

Correct answer:

(-1,-9)

Explanation:

A point is defined as (x,y) . If the point is shifted left or right, the value will be added or subtracted. If the point is shifted up or down, then the value will be added or subtracted.

3 units to the left is: x=2-3 =-1

5 units down is: y= -4-5 =-9

The new point is: (-1,-9)

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Example Question #302 : Geometry

Shift (-1,-1) up $\textup{3 units}$ and left $\textup{3 units}$ . State the new point.

Possible Answers:

(-4,2)

(3,2)

(2,-4)

(-3,-2)

(3,-4)

Correct answer:

(-4,2)

Explanation:

The movement of a point left and right will change the x-value of the point, as movement up and down will change the y-value of the point.

Three units up is adding three to the y-value.

(-1,-1+3) = (-1,2)

Left three units is subtracting three from the x-value.

(-1-3,2) = (-4,2)

The point is: (-4,2)

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Example Question #2083 : Hspt Mathematics

Begin at the point (3, -2) on the coordinate plane and move six units to the left. Where are you now?

Possible Answers:

(3, 4)

(3, -8)

(-3, -2)

(9, -2)

Correct answer:

(-3, -2)

Explanation:

Moving six units to the left changes the -coordinate of the point by subtracting six from it, while preserving the -coordinate. The ordered pair of the new location is (3-6, -2) , or (-3, -2) .

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : How To Find X Or Y Intercept

Example Question #2 : How To Find X Or Y Intercept

Example Question #3 : How To Find X Or Y Intercept

Example Question #1 : How To Find A Line On A Coordinate Plane

Example Question #2081 : Hspt Mathematics

Example Question #301 : Geometry

Example Question #302 : Geometry

Example Question #2082 : Hspt Mathematics

Example Question #302 : Geometry

Example Question #2083 : Hspt Mathematics

All HSPT Math Resources

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