The given triangle is a right triangle
The coordinates are given as:
D (0,n), E(m,n), F(m,0)
The length is calculated using:
[tex]l=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2[/tex]
So, we have:
[tex]DE=\sqrt{(0-m)^2 + (n-n)^2} = m[/tex]
[tex]DF=\sqrt{(0-m)^2 + (n-0)^2} = \sqrt{m^2 + n^2[/tex]
[tex]EF=\sqrt{(m-m)^2 + (n-0)^2} = n[/tex]
The slope is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]DE = \frac{n -n}{0- m} = 0[/tex]
[tex]DF = \frac{n -0}{0- m} = -\frac nm[/tex]
[tex]EF = \frac{n -0}{m- m} = \mathbf{unde fined}[/tex]
This is calculated using
[tex]m = 0.5 * (x_1 + x_2, y_1 + y_2)[/tex]
So, we have:
[tex]DE = 0.5 * (0 + m, n+ n)=(0.5m, n)[/tex]
[tex]DF = 0.5 * (0 + m, n+ 0)=(0.5m, 0.5n)[/tex]
[tex]EF = 0.5 * (m + m, n+ 0)=(m, 0.5n)[/tex]
In (a), we have:
Lengths
[tex]DE= m[/tex]
[tex]DF = \sqrt{m^2 + n^2[/tex]
[tex]EF= n[/tex]
Slope
[tex]DE = 0[/tex]
[tex]DF = -\frac nm[/tex]
[tex]EF = \mathbf{unde fined}[/tex]
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:
https://brainly.com/question/26331644
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