Question

Line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints an M1 (2,16) and M2 (-3,5) respectively. What is the distance between M1 and M2? Round to the nearest tenth

Answer 1

12.1

Explanation:

The dashed line joining M₁ and M₂ is the hypotenuse of a right triangle as shown in red below.

The base of the triangle is

x₂ - x₁ = 2 - (-3) = 2+ 3 = 5

The height of the triangle is

y₂ - y₁ = 16 - 5 = 11

We can now use Pythagoras' theorem to calculate distance between the two midpoints.

x² = 5² + 11² = 25 + 121 = 146

x = √146 = 12.1

The distance between M₁ and M₂ is 12.1.