Question

Fid the lengths of the sides of the triangle PQR. Is it right triangle? Is it an isosceles trianlge? (a) P(3,-2,-3), Q(7,0,1), R(1,2,1) (b) P(2,-1,0) Q(4,1,1), R(4,-5,4)

Answer 1

Explanation:

Vertices of the triangles are given by P, Q and R

To find the type of triangle

We use distance formula to find out the sides,PQ, QR and RP

Distance formula is

`√((x_2-x_1)^2 +(y_2-y_1)^2)+(z_2-z_1)^2)`

a) P(3,-2,-3), Q(7,0,1), R(1,2,1)

`PQ^2 = 16+4+16 =36\\QR^2 = 36+4 =40\\RP^2 = 4+16+16 = 36`

Since PQ = RP isosceles triangle

b) P(2,-1,0) Q(4,1,1), R(4,-5,4)

`PQ^2 = 9\\QR^2 = 45\\RP^2 = 36`

Since pythagorean theorem is satisfied, it is a right triangle.