Question

△ABC has vertices at A(−1, 4) , B(3, 1) , and C(0,−3) . Select from the drop-down menus to correctly complete the statements.

Answer 1

Given vertices of triangle ABC are A(−1, 4) , B(3, 1) , and C(0,−3).

Slope of AB is :

`m=(1-4)/(3-\left(-1\right)) = -(3)/(4)`

Slope of BC is :

`m=(-3-1)/(0-3)=(4)/(3)[/tex.</p><p>Slope of AC is: </p><p>[tex]m=(-3-4)/(0-\left(-1\right))=-7.`

Slope of AB is negative reciprocal of slope of BC.

Therefore, AB and BC are perpendicular lines and triangle ABC is a right triangle.

The slope of AB is -3/4, the slope of BC is 4/3, and the slope of AC is -7. Triangle ABC is a right triangle because two of these slopes have a product of -1.