SOLUTION: Triangle pqr has the given vertice classify the triangle by its sides. then determine if it is a right triangle p(2,0) q (6,6) and r (12,2)

Question 374261: Triangle pqr has the given vertice classify the triangle by its sides. then determine if it is a right triangle
p(2,0) q (6,6) and r (12,2)

Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
p(2,0) q (6,6) and r (12,2)

side length : |pq|=|(6-2,6-0)|=|(4,6)|=sqrt(16+36)=sqrt(52)

|pr|=|(12-2,2-0)|=|(10,2)|=sqrt(104)
|qr|=|(12-6,2-6)|=|(6,-4)|=sqrt(36+16)|=sqrt(52)

two sides are equal, it's an isoceles triangle.

angles : (dot product, if a.b=0 the 2 vectors are orthogonal)

pq.pr=40+12<>0

pq.qr=4*6-6*4=0 (for verif : pr*qr=60-8<>0)

hence the triangle is rectangle and has a right angle in q.

RELATED QUESTIONS
Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4).... (answered by josgarithmetic)

The coordinates of the vertices of ∆PQR are P (0,5), Q (5,0), and R (10,5).... (answered by mananth)

The coordinates of the vertices of ∆PQR are P (0,4), Q (4,0), and R (8,4) Determine... (answered by Alan3354,josgarithmetic)

If p, q and r are the sides opposite to the angles P, Q and R respectively in a triangle... (answered by ikleyn)

A triangle, PQR, has P(8, 0), Q(0, −8) and point R is on the line y = x − 2. Find the (answered by math_tutor2020)

a triangle has sides with measures 39,82,59,. Classify the triangle by its... (answered by Claire.123)

Analytic Geometry 1.a) Draw the triangle with vertices P(-2,-2), Q(2,4), and R(8,0).... (answered by Fombitz)

how that the triangle whose vertice are p(2,-2) Q(-4,-5) and R(8,9) is... (answered by algebrapro18)

A circle is centered at O and has an area of 48pi. Let Q and R be points on the circle,... (answered by Edwin McCravy,math_tutor2020)