Coordinate plane and distance — SHSAT practice questions

Coordinate plane and distance on the SHSAT Mathematics section covers midpoints on a number line and distances between points in the plane, including both a grid path of a horizontal segment then a vertical one and the straight-line segment joining the same points. A student has to recover a missing endpoint from a given midpoint, compare those two path lengths, and find the distance between two coordinates. Items are multiple choice with short setups; traps mix grid-path length with straight-line distance, drop a sign, or mishandle the midpoint. Choices are usually single numbers or simple algebraic values matching those errors.

Section: Mathematics 57 questions on the paper
84 practice questions in the app

Sample questions

Question 1

On a number line, the midpoint of the segment joining points $P(1)$ and $Q(x)$ is $M(5)$ . What is the value of $x$ ?

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Answer: C — 9

The midpoint equation is $\dfrac{1+x}{2}=5$ . Therefore, $1+x=10$ and $x=9$ .

Question 2

A path from $(0,0)$ to $(3,4)$ is a horizontal segment followed by a vertical segment. A second path is the straight-line segment joining the same points. How much longer, in units, is the first path than the second path?

A2 units
B5 units
C7 units
D12 units

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Answer: A — 2 units

The first path is $3+4=7$ units. The straight-line path is $\sqrt{3^2+4^2}=5$ units. So the first path is $7-5=2$ units longer.

Question 3

Points $A(-1,0)$ and $B(2,4)$ lie on a coordinate plane. What is the distance between the points?

A1 unit
B5 units
C6 units
D7 units

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Answer: B — 5 units

Use the coordinate differences as the legs of a right triangle: $\sqrt{3^2+4^2}=5$ .

Practice 84 Coordinate plane and distance questions in the app

Coordinate plane and distance — SHSAT practice questions

Sample questions

More SHSAT topics

Mathematics