Question

What is the length of the hypotenuse of the right angle defined by the points (-3,-1),(1,-1),and (1,2)?

A)square root of 3
B)square root of 3
C) 2 timessquare root of 3
D)5

Answer 1

To find the length of the triangle first find the two coordinates with a common x coordinate, (1,-1) and (1,2). Now find the difference between their y coordinates, -1 and 2. This means that the length of the triangle is 3.
To find the width of the triangle first find the two coordinates with a common y coordinate, (-3,-1) and (1,-1). Now find the difference between their x coordinates, -3 and 1. This means that the width of the triangle is 4.
By Pythagoras' theorem, we know that
`hypotenuse = \sqrt{ width^(2) + length^(2) }`. Inserting our newfound values into this equation, we an find thelength of the hypotenuse:

`hypotenuse = \sqrt{ 4^(2) +3^(2)} hypotenuse = √(16+9) hypotenuse = √(x) 25 hypotenuse = 5`
Therefore, your answer is D0 5. To visualise this question better, you can plot the points on a graph.