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Coordinate plane and distance — SHSAT practice questions

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Practice 84 Coordinate plane and distance questions in the app

What this topic is

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.

Sample questions

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

Question 1Easier

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

A4✗ Not this oneB6✗ Not this oneC9✓ CorrectD10✗ Not this one

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Answer: C — 9

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

Question 2Mid

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✓ CorrectB5 units✗ Not this oneC7 units✗ Not this oneD12 units✗ Not this one

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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 3Mid

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

A1 unit✗ Not this oneB5 units✓ CorrectC6 units✗ Not this oneD7 units✗ Not this one

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Answer: B — 5 units

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

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