Question

PLEASE HELP

Answer 1

The given triangle is a right triangle

The length and slope

The coordinates are given as:

D (0,n), E(m,n), F(m,0)

The length is calculated using:

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

So, we have:

$DE=\sqrt{(0-m)^2 + (n-n)^2} = m$

$DF=\sqrt{(0-m)^2 + (n-0)^2} = \sqrt{m^2 + n^2$

$EF=\sqrt{(m-m)^2 + (n-0)^2} = n$

The slope is calculated using:

$m = \frac{y_2 -y_1}{x_2 - x_1}$

So, we have:

$DE = \frac{n -n}{0- m} = 0$

$DF = \frac{n -0}{0- m} = -\frac nm$

$EF = \frac{n -0}{m- m} = \mathbf{unde fined}$

The coordinates of the midpoints

This is calculated using

$m = 0.5 * (x_1 + x_2, y_1 + y_2)$

So, we have:

$DE = 0.5 * (0 + m, n+ n)=(0.5m, n)$

$DF = 0.5 * (0 + m, n+ 0)=(0.5m, 0.5n)$

$EF = 0.5 * (m + m, n+ 0)=(m, 0.5n)$

The type of triangle

In (a), we have:

Lengths

$DE= m$

$DF = \sqrt{m^2 + n^2$

$EF= n$

Slope

$DE = 0$

$DF = -\frac nm$

$EF = \mathbf{unde fined}$

The sides are not equal.

However, the 0 and the undefined slope implies that the triangle is a right triangle because the sides are perpendicular

It should be noted that the triangle cannot be graphed because the coordinates are not numeric

Read more about triangles at:

brainly.com/question/26331644

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