Find PA and AC, givenP(0,0), C(-2,7)and A(2,5). Give exact answers in simplied radical form

Question

You are on the ground at P(0,0) and the campsite is at C(-2,7). You traveled around the mountain by going to A(2,5). The coordinate system is measured in meters. Draw a diagram of the situation. Find PA and AC. Give exact answer in simple radical form

Answer 1

sqrt is the square root function.

 

PA = sqrt( (2-0)^2 + (5-0)^2 ) = sqrt( 2^2 + 5^2 ) = sqrt ( 4 + 25) = sqrt(29)

 

AC = sqrt ( (-2 -2)^2 + (7-5)^2) = sqrt ( (-4)^2 + (2)^2) = sqrt ( 16 + 4) = sqrt(20) = sqrt(4 * 5) = 

                 sqrt(4) * sqrt(5) = 2 * sqrt(5)

 

 

PC = sqrt( (-2)^2 + (7)^2) = sqrt ( 4 + 49) = sqrt(53)

 

It is a scalene triangle