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Coordinate geometry — distance, midpoint, slope, line equations — ACT practice questions

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Practice 62 Coordinate geometry — distance, midpoint, slope, line equations questions in the app

What this topic is

Coordinate geometry — distance, midpoint, slope, line equations on the ACT Mathematics test asks students to work in the standard coordinate plane: find slope from two points, take the negative reciprocal for a perpendicular line, and write a line equation from intercepts.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

In the standard $(x,y)$ coordinate plane, line $k$ is perpendicular to a line whose slope is $\dfrac{2}{3}$. What is the slope of line $k$?

A$-\dfrac{3}{2}$✓ CorrectB$-\dfrac{2}{3}$✗ Not this oneC$\dfrac{2}{3}$✗ Not this oneD$\dfrac{3}{2}$✗ Not this one

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Answer: A — $-\dfrac{3}{2}$

Perpendicular lines have slopes that are negative reciprocals, so the slope of line $k$ is $-\dfrac{3}{2}$.

Question 2Easier

In the standard $(x,y)$ coordinate plane, a line contains the points $(3,-2)$ and $(7,10)$. What is the slope of that line?

A$\dfrac{1}{3}$✗ Not this oneB2✗ Not this oneC3✓ CorrectD4✗ Not this one

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Answer: C — 3

The slope is $\dfrac{10-(-2)}{7-3}=\dfrac{12}{4}=3$.

Question 3Easier

A line in the standard $(x,y)$ coordinate plane crosses the $x$-axis at 4 and the $y$-axis at $-2$. Which of the following is an equation of this line?

A$y=-\dfrac{1}{2}x-2$✗ Not this oneB$y=2x-2$✗ Not this oneC$y=\dfrac{1}{2}x-2$✓ CorrectD$y=\dfrac{1}{2}x+2$✗ Not this one

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Answer: C — $y=\dfrac{1}{2}x-2$

The line passes through $(0,-2)$ and $(4,0)$, giving a slope of $\dfrac{0-(-2)}{4-0}=\dfrac{1}{2}$. Its equation is therefore $y=\dfrac{1}{2}x-2$.

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