Step-by-step explanation:
To find the distance between two points, we have to use the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
Let's solve for line PQ first. We plug in the points into the formula and solve from there.
P: (-5, 1)
Q: (-2, -5)
[tex]PQ=\sqrt{(-2+5)^2+(-5-1)^2 }[/tex]
[tex]PQ=\sqrt{(3)^2+(-6)^2 }[/tex]
[tex]PQ=\sqrt{9+36}[/tex]
[tex]PQ=\sqrt{45}[/tex]
[tex]PQ=3\sqrt{5}[/tex]
Now, let's solve line ML.
M: (5, 3)
L: (2, -3)
[tex]ML=\sqrt{(2-5)^2+(-3-3)^2 }[/tex]
[tex]ML=\sqrt{(-3)^2+(-6)^2}[/tex]
[tex]ML=\sqrt{9+36}[/tex]
[tex]ML=\sqrt{45}[/tex]
[tex]ML=3\sqrt{5}[/tex]
Answer: 3√5, 3√5, yes, they are congruent.
