Coordinate Geometry Practice Questions on the ACT

By Lisa Zimmer Hatch, Scott A. Hatch

The ACT Math Test contains questions on coordinate geometry, which require that you know things like the midpoint and distance formulas for points on an x, y–coordinate graph. Here are a couple of examples for you to try.

Sample questions

  1. What coordinate point is the midpoint of the line segment that goes from point (–1, 3) to point (5, –5) in the standard (x, y) coordinate plane?

    (A) (–3, 4)

    (B) (2, –1)

    (C) (3, –1)

    (D) (2, 4)

    (E) (–1, –5)

  2. What is the distance in the standard (x, y) coordinate plane between the points (–6, 1) and (2, 7)?

    (F)

    image0.png

    (G)

    image1.png

    (H) 10

    (J) 8

    (K) 6

Answers and explanations

  1. 1. The correct answer is Choice (B).

    To find the midpoint of a line segment, find the average of both the x and y coordinates of the endpoints. The average of the x-coordinates is half of –1 + 5, which is 2. Eliminate any answer that doesn’t have an x-coordinate of 2. That leaves you with Choices (B) and (D). Find the midpoint of the y-coordinates. Half of 3 – 5 is –1.

    If you picked Choice (A), you found the difference between the points instead of the sum.

  2. 2. The correct answer is Choice (H).

    One way to solve this question is by plugging the given values into the distance formula and solving:

    image2.png

    If you don’t remember the distance formula, don’t fret! Draw the given points on a makeshift coordinate plane. Draw a line over from the point (–6, 1) over to the point (2, 1). Then, draw a line up from the point (2, 1) to the point (2, 7) to make a right triangle with the two given points as vertices of the non-right angles. Then you can see that the legs of the triangle are length 6 and length 8, so you know the diagonal has to be length 10 because it is a 3-4-5 right triangle.

    Make sure you’re familiar with the distance formula because you’re almost guaranteed to see a problem that requires you to use it on the ACT.