Question

Ke Shawn is placing a right triangle in the coordinate plane. He knows that the longer leg is twice the length of the shorter leg. He places the longer leg on the x-axis.

What coordinates should he assign to the third vertex of the triangle?

Answer 1

The third vertex of triangle is (2a,0)

Explanation:

We are given the following information in the question:

A right angled triangle such the longer side is twice the length of the shorter side.

We have to find the coordinate of the third vertex of triangle.

Let A(0,a), B(0,0), C(x,0)

Distance between two points with coordinate
`(x_1,y_1), (x_2,y_2)` is given by:

`√((x_2-x_1)^2 + (y_2-y_1)^2)`

Now, we are given that the longer side is twice the length of the shorter side.

Thus, we can write:

`AC = 2AB\\√((x-0)^2 + (0-0)^2)= 2√((0-0)^2 + (a-0)^2)\\\pm x = \pm 2a\\\text{Since the point lies on the positive side of x-axis}\\x = 2a`

The third vertex of triangle is (2a,0)

Answer 2

the 3rd vertex is on the x axis line which means Y =0

since the longer leg is twice as long as the shorter leg and the length of the shorter leg is a, then twice the length would be 2a ( 2 times a)

so the 3rd vertex is (2a,0)