Question

the vertices of a triangle at A(5,-4) ,B(7,0) ,and C(1,-2). if the triangle is a right triangle, which vertex is the right angle

Answer 1

We can find the right angle of the triangle by finding the slope of the sides .

Any right angle makes an angle of 90 degrees and the lines are perpendicular .

For perpendicular lines product of slopes is -1.

In other words the slopes have opposite signs and are reciprocal .

Let us find the slopes of AB,BC,CA.

Slope of two points can be found by the difference in y values divided by different in x values

Slope of AB=$\frac{0+4}{7-5} =\frac{4}{2} =2$

Slope of BC=$\frac{-2-0}{1-7} =\frac{-2}{-6} = 3$

Slope of CA=$\frac{-2+4}{1-5} =\frac{2}{-4} =\frac{-1}{2}$

The slopes of AB and CA are reciprocal of each other with opposite signs or we can say their product is -1 so they are perpendicular.

Angle A is the common angle to these sides so we say angle A is the right angle