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

Distance between two points on the coordinate plane comes from the Pythagorean theorem: the horizontal and vertical differences form the legs of a right triangle, and the distance is the hypotenuse.

The midpoint of a segment is found by averaging the coordinates, and a reverse question gives one endpoint and the midpoint and asks for the other endpoint. Coordinate plane and distance questions can also compare a path that follows grid lines with the straight-line path between the same points, which is shorter unless the points lie on one grid line.

Sign errors are the most frequent slip, especially when subtracting a negative coordinate.

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 $x$ ?

4✗ Not this one6✗ Not this one9✓ Correct10✗ Not this one

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Answer: C — 9

The midpoint equation is $\frac{1 + x}{2} = 5$ . 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?

2 units✓ Correct5 units✗ Not this one7 units✗ Not this one12 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, in units, between the points?

1 unit✗ Not this one5 units✓ Correct6 units✗ Not this one7 units✗ Not this one

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Answer: B — 5 units

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

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

Practice 84 Coordinate plane and distance questions in the app

Coordinate plane and distance — SHSAT practice questions

What this topic is

Sample questions

More SHSAT topics

Mathematics