Practice Distance on the Coordinate Plane in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The distance between two points on the coordinate plane is found using the Pythagorean theorem: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Draw a right triangle between the two points — the horizontal and vertical distances are the legs, and the straight-line distance is the hypotenuse.

Showing a random 20 of 50 problems.

Example 1

medium
Find the distance between (−5,2)(-5,2) and (3,−4)(3,-4).

Example 2

medium
Three points: A(0,0), B(4,0), C(4,3)A(0,0),\ B(4,0),\ C(4,3). Is triangle ABCABC a right triangle?

Example 3

challenge
Find the point on the yy-axis equidistant from (3,4)(3,4) and (5,−2)(5,-2).

Example 4

medium
Find the midpoint distance: from (0,0)(0,0) to the midpoint of (4,0)(4,0) and (0,6)(0,6).

Example 5

easy
Find the distance between (1,2)(1,2) and (1,−6)(1,-6). Show the shortcut for vertical segments.

Example 6

medium
Find the distance between (1,4)(1,4) and (6,16)(6,16).

Example 7

hard
Quadrilateral has vertices (0,0),(4,0),(4,3),(0,3)(0,0),(4,0),(4,3),(0,3). Find the length of each diagonal.

Example 8

easy
Find the distance between (−1,−1)(-1,-1) and (2,3)(2,3).

Example 9

medium
A delivery robot travels from (0,0)(0,0) to (8,6)(8,6) in a straight line. How far does it go?

Example 10

medium
Is the triangle with vertices (0,0)(0,0), (5,0)(5,0), (0,5)(0,5) isosceles? Use distances.

Example 11

medium
Find the distance between (3,−2)(3,-2) and (−1,1)(-1,1).

Example 12

easy
Find the distance between (−2,−3)(-2,-3) and (−2,4)(-2,4).

Example 13

hard
A circle has center (2,−1)(2,-1) and radius 5. Determine whether (5,3)(5,3) is inside, on, or outside the circle.

Example 14

easy
What is the distance from (5,12)(5,12) to the origin?

Example 15

medium
Find x so that (x,0)(x,0) is exactly 13 units from (0,5)(0,5).

Example 16

easy
Find the distance between (1,2)(1,2) and (4,6)(4,6).

Example 17

medium
Find the perimeter of the triangle with vertices (0,0)(0,0), (4,0)(4,0), (4,3)(4,3).

Example 18

challenge
Verify whether (0,0)(0,0), (5,0)(5,0), (2,4)(2,4) form an isosceles triangle, and identify which sides (if any) are equal.

Example 19

hard
Find the perimeter of triangle with vertices (−1,−1),(2,3),(5,−1)(-1,-1),(2,3),(5,-1).

Example 20

medium
Find the distance between (2,1)(2,1) and (5,5)(5,5) in simplest form.
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