Find the lengths of the sides of the triangle with the vertices 𝐴(2,−1,4), 𝐵(−2,2,9), and 𝐶(6,4,7)

Question

|AB|= ?

|AC|= ?

|BC|=?

is triangle ABC an isosceles triangle?

Answer 1

AB = sqr(16 +9 + 25) = sqr50= 5sqr2

AC = sqr(16 + 25 + 9) = 5sqr2

BC = sqr(64 + 4 + 4) = sqr72 = 6sqr2

It's isosceles since AB = AC

d =sqr [(x1-x2)^2 + (y1-y2)^2 + (z1-z2)] is the formula for finding distance from (x1,y1,z1) to (x2,y2,z2)

distance = square root of the sum of squares of the differences in coordinates