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HSPT Math : Geometry

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Example Questions

Example Question #291 : Geometry

In which quadrant, or on which axis, is the point with coordinates (6,-6) located?

Possible Answers:

The -axis

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Correct answer:

Quadrant IV

Explanation:

Any point with a positive -coordinate and a negative -coordinate is located in the lower right quadrant - Quadrant IV.

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Example Question #292 : Geometry

Which of the following is an equation of a line with slope 0?

Possible Answers:

x = 6

x+y= 10

$y=x^{2} +1$

y = -5

y = x+7

Correct answer:

y = -5

Explanation:

A line with slope 0 has equation y = b for some real value .

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Example Question #293 : Geometry

Axes

Give the equation of the red line in slope-intercept form.

Possible Answers:

$y = -\frac{4}{7}x + 6$

$y =- \frac{7}{4}x + 6$

$y = \frac{7}{4}x + 6$

$y = \frac{4}{7}x + 6$

$y =- \frac{7}{4}\left (x + 6 \right )$

Correct answer:

$y = \frac{7}{4}x + 6$

Explanation:

The slope of the line is

$m = \frac{y_{2}- y_{1}}{x_{2}- x_{1}} = \frac{6- (-1)}{0-(-4)} = \frac{7}{4}$

The -intercept of the line has -coordinate b= 6

The slope-intercept form can be written:

y = mx+b

Replace:

$y = \frac{7}{4}x+6$

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Example Question #294 : Geometry

Axes_2

The green and blue lines are perpendicular: What is the slope of the blue line?

Possible Answers:

It cannot be determined from the information given.

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

The slope of the blue line, being perpendicular to the green line, is the opposite of the reciprocal of the slope of the green line. The slope of the green line can be found using the slope formula:

$m = \frac{y_{2}- y_{1}}{x_{2}- x_{1}} = \frac{10-0}{0-30} = -\frac{1}{3}$

The opposite of the reciprocal of $-\frac{1}{3}$ is 3, and this is the slope of the blue line.

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Example Question #1 : Midpoint Formula

A line segment on the coordinate plane has endpoints (a-5,-b) and (b+8, a-4) . In terms of and , as applicable, give the -coordinate of its midpoint.

Possible Answers:

$\frac{a - b - 13}{2}$

$\frac{a + b + 3}{2}$

a - b - 4

$\frac{a - b - 4}{2}$

a + b + 3

Correct answer:

$\frac{a + b + 3}{2}$

Explanation:

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$x= \frac{(a-5)+(b+8)}{2} = \frac{a+b-5+8}{2} = \frac{a+b+3}{2}$ .

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Example Question #295 : Geometry

A line segment on the coordinate plane has endpoints (a-5,-b) and (b+8, a-4) . In terms of and , as applicable, give the -coordinate of its midpoint.

Possible Answers:

$\frac{a + b + 3}{2}$

a + b + 3

$\frac{a + b - 4}{2}$

a - b - 4

$\frac{a - b - 4}{2}$

Correct answer:

$\frac{a - b - 4}{2}$

Explanation:

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$y= \frac{(a-4)+(-b)}{2} = \frac{a-b-4}{2}$ .

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Example Question #296 : Geometry

A line segment on the coordinate plane has midpoint $\left ( A + 5, B + 7\right )$ . One of its endpoints is $\left ( 10, 6 \right )$ . What is the -coordinate of the other endpoint, in terms of and/or ?

Possible Answers:

B + 8

2B + 8

B + 1

2B + 20

2B + 1

Correct answer:

2B + 8

Explanation:

Let be the -coordinate of the other endpoint. Since the -coordinate of the midpoint of the segment is the mean of those of the endpoints, we can set up an equation as follows:

$\frac{Y + 6 }{2} = B + 7$

$\frac{Y + 6 }{2} \cdot 2= \left ( B + 7 \right )\cdot 2$

Y + 6 = 2B + 14

Y + 6 -6 = 2B + 14 -6

Y = 2B + 8

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Example Question #297 : Geometry

A line segment on the coordinate plane has one endpoint at $\left ( 8, 10 \right )$ ; its midpoint is $\left ( A+B, A- B\right )$ . Which of the following gives the -coordinate of its other endpoint in terms of and ?

Possible Answers:

A + B- 16

2 A + 2B+8

A + B+8

2 A + 2B- 8

A + B- 8

Correct answer:

2 A + 2B- 8

Explanation:

To find the value of the -coordinate of the other endpoint, we will assign the variable . Then, since the -coordinate of the midpoint of the segment is the mean of those of its endpoints, the equation that we can set up is

$\frac{T + 8 }{2} = A + B$ .

We solve for :

$\frac{T + 8 }{2} \cdot 2 =\left ( A + B \right )\cdot 2$

T + 8 =2 A + 2B

T + 8 - 8 =2 A + 2B- 8

T =2 A + 2B- 8

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Example Question #298 : Geometry

Two perpendicular lines intersect at the point (5,4) . One line passes through point (3,1) ; the other passes through point $\left ( 4, Y\right )$ . Evaluate .

Possible Answers:

$Y = 2\frac{1}{2}$

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

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

$Y = 4\frac{2}{3}$

$Y = 5\frac{1}{2}$

Correct answer:

$Y = 4\frac{2}{3}$

Explanation:

The line that passes through $\left ( 3,1\right )$ and $\left ( 5,4\right )$ has slope

$m = \frac{4-1}{5-3} = \frac{3}{2}$ .

The line that passes through $\left ( 4, Y\right )$ and (5,4) , being perpendicular to the first, has as its slope the opposite reciprocal of $\frac{3}{2}$ , or $-\frac{2}{3}$ .

Therefore, to find , we use the slope formula and solve for :

$-\frac{2}{3} = \frac{Y-4}{4-5}$

$-\frac{2}{3} = \frac{Y-4}{-1}$

$-\frac{2}{3} \cdot (-1) = \frac{Y-4}{-1} \cdot (-1)$

$\frac{2}{3}= Y-4$

$\frac{2}{3}+ 4= Y-4 + 4$

$4\frac{2}{3}= Y$

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Example Question #299 : Geometry

What is the -intercept of the graph of the function $f \left ( x\right ) = 2x^{2} - 7x + 5$ ?

Possible Answers:

$\left (0,2 \right )$

$\left (0,-7 \right )$

$\left (0,0 \right )$

$\left (0,5 \right )$

$\left ( 0, -3 \frac{1}{2}\right )$

Correct answer:

$\left (0,5 \right )$

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis - that is, at which x = 0 . This point is $\left (0, f(0) \right )$ , so evaluate f(0) :

$f \left ( x\right ) = 2x^{2} - 7x + 5$

$f \left (0\right ) = 2 \cdot 0^{2} - 7 \cdot 0 + 5$

$f \left (0\right ) = 0- 0 + 5 = 5$

The -intercept is $\left (0,5 \right )$ .

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #291 : Geometry

Example Question #292 : Geometry

Example Question #293 : Geometry

Example Question #294 : Geometry

Example Question #1 : Midpoint Formula

Example Question #295 : Geometry

Example Question #296 : Geometry

Example Question #297 : Geometry

Example Question #298 : Geometry

Example Question #299 : Geometry

All HSPT Math Resources

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