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=
`(0+4)/(7-5) =(4)/(2) =2`

Slope of BC=
`(-2-0)/(1-7) =(-2)/(-6) = 3`

Slope of CA=
`(-2+4)/(1-5) =(2)/(-4) =(-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