Coordinate geometry (midpoint, distance) — ISEE Upper practice questions

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Practice 88 Coordinate geometry (midpoint, distance) questions in the app

What this topic is

Coordinate geometry (midpoint, distance) on the ISEE Upper Mathematics Achievement section covers midpoints, distances between points, axis reflections, and perpendicular lines in the plane.

A student must find a midpoint from two endpoints, compute distance, including vertical distance, reflect a point across an axis, and identify which point lies on a line perpendicular to a given line through a given point. Items usually ask for a point, a distance, or a reflected pair, with other points or lengths as choices; traps include swapping coordinates, reflecting across the wrong axis, and using a parallel slope instead of the negative reciprocal.

Sample questions

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

Question 1Mid

Line $k$ passes through $(2,-1)$ and $(8,3)$ . Which point lies on a line perpendicular to $k$ that passes through $(2,-1)$ ?

(6,5)

✗ Not this one

(-4,7)

✗ Not this one

(-4,-5)

✗ Not this one

(6,-7)

✓ Correct

Show answer

Answer: D — $(6,-7)$

The slope of $k$ is $\dfrac{3-(-1)}{8-2}=\dfrac46=\dfrac23$ . A perpendicular line has slope $-\dfrac32$ . From $(2,-1)$ to $(6,-7)$ , the slope is $\dfrac{-7-(-1)}{6-2}=\dfrac{-6}{4}=-\dfrac32$ , so $(6,-7)$ lies on the perpendicular line.

Question 2Easier

What is the reflection of $(2,6)$ across the $x$ -axis?

(-2,6)

✗ Not this one

(2,-6)

✓ Correct

(-2,-6)

✗ Not this one

(6,2)

✗ Not this one

Show answer

Answer: B — $(2,-6)$

Reflection over the $x$ -axis keeps x and negates y, producing $(2,-6)$ .

Question 3Easier

What is the vertical distance between $R(-2,2)$ and $S(-2,8)$ ?

5✗ Not this one6✓ Correct7✗ Not this one8✗ Not this one

Show answer

Answer: B — 6

The x-coordinates match, so distance is $|8-(2)|=6$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 88 Coordinate geometry (midpoint, distance) questions in the app

Coordinate geometry (midpoint, distance) — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Mathematics Achievement