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HSPT Math : Concepts

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Example Questions

Example Question #2081 : Hspt Mathematics

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)

(-1,1)

(3,5)

(1,-9)

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 #2083 : Hspt Mathematics

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

Possible Answers:

(2,-4)

(-4,2)

(3,2)

(-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 #2084 : 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, -8)

(3, 4)

(9, -2)

(-3, -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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Example Question #2085 : Hspt Mathematics

Begin at the point (1, - 5) on the coordinate plane and move four units to the right. Next, move six units up. Where are you now?

Possible Answers:

(-3, -11)

(5, 1)

(-5, -9)

(7, -1)

Correct answer:

(5, 1)

Explanation:

Moving four units to the right increases the -coordinate by 4; moving six units up increases the -coordinate by 6. The current location is

(1+4, - 5+6) , or (5, 1) .

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Example Question #2086 : Hspt Mathematics

On the coordinate plane, how do you get from (-3, 4) to (7, 2) ?

Possible Answers:

Move up ten units and right two units

Move right ten units and down two units

Move down ten units and left two units

Move left ten units and up two units

Correct answer:

Move right ten units and down two units

Explanation:

The -coordinate changes by 7 - (-3) = 10 units; therefore, you must move ten units in a positive horizontal direction - right.

The -coordinate changes by 2 - 4 = -2 units; therefore, you must move two units in a negative vertical direction - down.

The correct response is to move right ten units and down two units.

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Example Question #1491 : Concepts

How far from the origin is the point (-16, 12) on the coordinate plane?

Possible Answers:

Correct answer:

Explanation:

Apply the distance formula, substituting the -coordinates for $x_{1}$ and $x_{2}$ and the -coordinates for $y_{1}$ and $y_{2}$ :

$d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

$= \sqrt{(-16-0)^{2}+(12-0)^{2}}$

$= \sqrt{(-16)^{2}+12^{2}}$

$= \sqrt{256+144}$

$= \sqrt{400}$

= 20

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Example Question #2092 : Hspt Mathematics

Two lines on the coordinate plane are perpendicular and intersect at the origin. One has slope $\frac{3}{7}$ . Give the equation of the other.

Possible Answers:

3x + 7 y = 0

3x-7 y = 0

7x + 3 y = 0

7x-3 y = 0

Correct answer:

7x + 3 y = 0

Explanation:

A line perpendicular to a line with slope $\frac{3}{7}$ has as its slope the opposite of the reciprocal of $\frac{3}{7}$ ; this number is $- \frac{7}{3}$ . The line passes through the origin, which is the point (0,0) ; this is also the -intercept. In slope-intercept form, its equation can be found by substituting $m = - \frac{7}{3}, b= 0$ in the equation:

y = m x+ b

$y = - \frac{7}{3}x+ 0$

$y = - \frac{7}{3}x$

This can be rewritten in standard form as follows:

$y+ \frac{7}{3}x = - \frac{7}{3}x + \frac{7}{3}x$

$\frac{7}{3}x + y= 0$

$3 \left (\frac{7}{3}x + y \right )=3 \cdot 0$

$3 \cdot \frac{7}{3}x + 3 \cdot y = 0$

7x + 3 y = 0

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Example Question #1492 : Concepts

A line with slope passes through the origin and the point (16, N) . Evaluate .

Possible Answers:

$N = -\frac{1}{4}$

N = 12

N = -4

N = -64

Correct answer:

N = -64

Explanation:

The origin is (0,0) . In the following slope formula, set

$x_{2} = 16, y_{2}= N, x_{1} = y_{1}= 0, m = -4$ ,

and solve for :

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

$-4 = \frac{N-0}{16-0}$

$-4 = \frac{N}{16}$

$-4\cdot 16 = \frac{N}{16} \cdot 16$

-64 = N

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Example Question #2093 : Hspt Mathematics

The lines of which two of the following equations are perpendicular to each other?

(I) y = 8

(II) x= 8

(III) x+ y = 8

Possible Answers:

II and III

I and II

I and III

No two of the equations given are represented by lines that are perpendicular to each other.

Correct answer:

I and II

Explanation:

y = 8 and x= 8 are represented by a horizontal line and a vertical line, respectively; therefore, their graphs are perpendicular.

As for the third equation, x+ y = 8 , this is represented by a line with slope , as seen below:

x+ y = 8

x+ y -x = 8 - x

y = -x+8

y = -1x+8

The equation is in slope-intercept form, and the slope of the line is the coefficient of , which is . It is perpendicular to a line with slope $- \frac{1}{-1} = 1$ ; however, the horizontal line has slope 0, and the vertical line has undefined slope.

The correct choice is therefore I and II.

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #2081 : Hspt Mathematics

Example Question #2082 : Hspt Mathematics

Example Question #2083 : Hspt Mathematics

Example Question #2084 : Hspt Mathematics

Example Question #2085 : Hspt Mathematics

Example Question #2086 : Hspt Mathematics

Example Question #1491 : Concepts

Example Question #2092 : Hspt Mathematics

Example Question #1492 : Concepts

Example Question #2093 : Hspt Mathematics

All HSPT Math Resources

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