Using slope formulas, we can conclude that Lydia's assertion is incorrect.
The coordinates of the triangle are given as:
[tex]D = (- 2, - 1)[/tex]
[tex]E= (- 2, 2)[/tex]
[tex]F =(0, 0)[/tex]
Start by calculating the slopes of lines DF and EF using the following slope formula
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{DF} = \frac{-1 -0}{-2 -0}[/tex]
[tex]m_{DF} = \frac{1}{2}[/tex]
Next, we calculate the slope of EF
[tex]m_{EF} = \frac{2 - 0}{-2 - 0}[/tex]
[tex]m_{EF} = -1[/tex]
For the triangle to be a right-angled, the following must be true
[tex]m_{EF} \times m_{DF}= -1[/tex]
So, we have:
[tex]-1 \times \frac 12= -1[/tex]
[tex]-\frac 12= -1[/tex]
The above equation is not true.
Hence, Lydia's assertion is incorrect.
Read more about right triangles at:
https://brainly.com/question/14517390
