Question

What is the length of the shortest side of a triangle that has vertices at (-2, 5), (-2, -7), and (-6, -4)?

A. 9 units


B. 2√5 units


C. √7 units


D. 5 units

Answer 1

D. 5 units

Explanation:

To work out the length use formula:

`length = \sqrt{(y₂-y1) {}^(2) + (x₂-x1) {}^(2)}`

length of AB:

`AB = \sqrt{( - 4 - 5) {}^(2) + ( - 6 - ( - 2)) {}^(2) } = √(97)`

length of AC:

`AC = \sqrt{( - 7 - 5) {}^(2) + ( - 2 - ( - 2)) {}^(2) } = 12`

length of BC:

`BC = \sqrt{( - 7 - ( - 4)) {}^(2) + ( - 2 - ( - 6)) {}^(2) } = 5`

as you can see BC has the shortest side of 5 units