Question

On a piece of graph paper, plot the following points: A (0, 0), B (5, 0), and C (2, 4). These coordinates will be the vertices of a triangle. How would you use the distance formula to determine what kind of triangle this is? Is the triangle equilateral, right, or scalene? Now use the midpoint formula to determine the midpoints of the triangle's sides: segments AB, BC, and CA. Connect the midpoints to make four triangles within the first triangle. Are these four triangles similar?

Answer 1

The triangle is an isosceles triangle and the four triangles are similar

How to determine the triangle type?

The coordinates are given as:

A (0, 0), B (5, 0), and C (2, 4).

Calculate the distance between the coordinates using:

$d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2$

So, we have:

$AB = \sqrt{(0 -5)^2 +(0-0)^2} =5$

$AC = \sqrt{(0 -2)^2 +(0-4)^2} =4.5$

$BC = \sqrt{(5 -2)^2 +(0-4)^2} =5$

The above shows that two sides are congruent.

Hence, the triangle is an isosceles triangle

The midpoints of the sides

This is calculated using:

(x, y) = 0.5 * (x1 + x2, y1 + y2)

So, we have:

AB = 0.5 * (0 + 5, 0 + 0) = (2.5, 0)

AC = 0.5 * (0 + 2, 0 + 4) = (1, 2)

BC = 0.5 * (5 + 2, 0 + 4) = (3.5, 2)

From the attached graph, we can see that the triangles are similar

Read more about similar triangles at:

brainly.com/question/14285697

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