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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?

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 class=

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grantgreving1

Answer:

(2a, 0)

Step-by-step explanation:

the length of the short side times 2 would equal the long side. We know this because the question says: "the longer leg is twice the length of the shorter leg". And the length of the short side is "a". so 2 times the length of the shorter leg, "a", equals the longer side: 2 • a = longer side or 2a. Since the side is on the x-axis, 2a is the first coordnate. Then, the side is exactly on the x-axis so the y-coordnate is 0. (2a, 0)

Don't believe me? here I did the test:

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MrRoyal

The coordinates of a triangle are the position of the endpoints of the triangle

The coordinates of the third vertex is (2a, 0)

The coordinates of the triangle are:

[tex]\mathbf{A = (0,a)}[/tex]

[tex]\mathbf{B = (0,0)}[/tex]

Because the longer leg is on the x-axis, the y-coordinate will be 0.

So, we have:

[tex]\mathbf{C = (x,0)}[/tex]

Calculate distance AB

[tex]\mathbf{AB = \sqrt{(0 - 0)^2 + (0 - a)^2}}[/tex]

[tex]\mathbf{AB = a}[/tex]

Calculate distance BC

[tex]\mathbf{BC = \sqrt{(0 - x)^2 + (0 - 0)^2}}[/tex]

[tex]\mathbf{BC = x}[/tex]

The longer leg is twice the shorter leg.

So:

[tex]\mathbf{BC = 2BA}[/tex]

Substitute values for BC and BA

[tex]\mathbf{x = 2a}[/tex]

Hence, the coordinates of the third vertex is (2a, 0)

Read more about vertices of a triangle at:

https://brainly.com/question/14815086

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