Use a coordinate grid to write a coordinate proof of the following statement.
If the vertices of a triangle are A(0,0), B(2 a, b) , and C(4 a, 0) , then the triangle is isosceles.
a. Plot the vertices on a coordinate grid to model the problem.

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VidyaaTech2022 VidyaaTech2022 · Answer 1 · 2022-09-14T12:23:26+02:00

Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

And, The vertices on a coordinate are plot in figure.

Here,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

And, Plot the vertices on a coordinate grid to model the problem.

What is Isosceles triangle?

When two sides of a triangle are equal then the triangle is said to be isosceles triangle.

Now,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

For this we use distance formula and prove that the two sides of triangle are equal.

Distance between the points A (0, 0) and B (2a, b) is;

[tex]D_{AB} = \sqrt{(2a - 0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]

And, Distance between the points B (2a, b) and C (4a, 0) is;

[tex]D_{BC} = \sqrt{(4a - 2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

Hence, Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

a. The vertices are plot in coordinate grid to model the problem in figure.

Learn more about the isosceles triangle visit:

brainly.com/question/1475130

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