find the perimeter of triangle with vertices A(-7,1), B(-3,1), C(-7,4)

Question

Is there a shorter way to calculate it without using the distance formula each time?

Answer 1

Draw a diagram. 

 

A and C have the same x-coordinate, so AC = 4-1 = 3

 

A and B have the same y-coordinate, so AB = -3 - (-7) = 4

 

A, B, and C are the vertices of a right triangle.  BC is the hypotenuse.

 

By the distance formula (or using the Pythagorean Theorem), BC = 5

 

So, perimeter = 3+4+5 = 12