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SSAT Upper Level Math : Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #3 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points lies on the line with the equation $y=\frac{1}{3}x-3$ ?

Possible Answers:

(6, 2)

(-6, 8)

(3, -2)

(-3, 0)

Correct answer:

(3, -2)

Explanation:

To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.

For x=3 ,

$y=3(\frac{1}{3})-3=1-3=-2$

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Example Question #4 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points lies on the line with the equation $y=\frac{1}{4}x-2$ ?

Possible Answers:

(4, 3)

(-12, -5)

(0, 5)

(-4, 9)

Correct answer:

(-12, -5)

Explanation:

For x=-12 ,

$y=-12(\frac{1}{4})-2=-3-2=-5$

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Example Question #5 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points lies on the line with the equation y=-2x+4 ?

Possible Answers:

(-2, 8)

(-1, -5)

(0, 3)

(2, 1)

Correct answer:

(-2, 8)

Explanation:

For x=-2 ,

y=-2(-2)+4=8

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Example Question #6 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points is on the line with the equation y=3x-2 ?

Possible Answers:

(5, 15)

(-3, 7)

(3, 7)

(2, 0)

Correct answer:

(3, 7)

Explanation:

For x=3 ,

y=3(3)-2=7

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Example Question #2 : How To Find Out If A Point Is On A Line With An Equation

Consider the lines described by the following two equations:

4y = 3x²

3y = 4x²

Find the vertical distance between the two lines at the points where x = 6.

Possible Answers:

Correct answer:

Explanation:

Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:

Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.

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Example Question #3 : Other Lines

For the line

$y=\frac{1}{3}x-7$

Which one of these coordinates can be found on the line?

Possible Answers:

(3, –6)

(9, 5)

(6, –12)

(6, 5)

(3, 7)

Correct answer:

(3, –6)

Explanation:

To test the coordinates, plug the x-coordinate into the line equation and solve for y.

y = 1/3x -7

Test (3,-6)

y = 1/3(3) – 7 = 1 – 7 = -6 YES!

Test (3,7)

y = 1/3(3) – 7 = 1 – 7 = -6 NO

Test (6,-12)

y = 1/3(6) – 7 = 2 – 7 = -5 NO

Test (6,5)

y = 1/3(6) – 7 = 2 – 7 = -5 NO

Test (9,5)

y = 1/3(9) – 7 = 3 – 7 = -4 NO

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Example Question #52 : Lines

Solve the following system of equations:

–2x + 3y = 10

2x + 5y = 6

Possible Answers:

(3, 5)

(2, 2)

(3, –2)

(–2, –2)

(–2, 2)

Correct answer:

(–2, 2)

Explanation:

Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)

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Example Question #51 : Coordinate Geometry

Which of the following sets of coordinates are on the line $y=3x-4$ ?

Possible Answers:

$(2,2)$

$(1,5)$

$(3,4)$

$(1,2)$

$(2,-2)$

Correct answer:

$(2,2)$

Explanation:

$(2,2)$ when plugged in for $y$ and $x$ make the linear equation true, therefore those coordinates fall on that line.

$y=3x-4$

2=3(2)-4

2=6-4

2=2

Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.

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Example Question #52 : Coordinate Geometry

Which of the following points can be found on the line $\small y=3x+2$ ?

Possible Answers:

(-1,2)

(1, 5)

(2, 7)

(0, 1)

(1, 0)

Correct answer:

(1, 5)

Explanation:

We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.

y=3x+2

5=3(1)+2

5=3+2

5=5

Because this equality is true, we can conclude that the point (1,5) lies on this line. None of the other given answer options will result in a true equality.

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Example Question #1 : How To Find Out If Lines Are Perpendicular

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:

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

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

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

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

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

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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #3 : How To Find Out If A Point Is On A Line With An Equation

Example Question #4 : How To Find Out If A Point Is On A Line With An Equation

Example Question #5 : How To Find Out If A Point Is On A Line With An Equation

Example Question #6 : How To Find Out If A Point Is On A Line With An Equation

Example Question #2 : How To Find Out If A Point Is On A Line With An Equation

Example Question #3 : Other Lines

Example Question #52 : Lines

Example Question #51 : Coordinate Geometry

Example Question #52 : Coordinate Geometry

Example Question #1 : How To Find Out If Lines Are Perpendicular

All SSAT Upper Level Math Resources

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