Show that A(6,4), B(5,-2) and C(7,-2) are the vertices of an isosceles triangle Also, find the length of the - Maths - Coordinate Geometry

Question

​Show that A(6,4), B(5,-2) and C(7,-2) are the vertices of an
isosceles triangle Also, find the length of the median through A

Lovina Kansal · Accepted Answer

Dear student
We have,A6,4,B5,-2 and C7,-2Now, AB=5-62+-2-42=1+36=37BC=7-52+-2+22=4=2CA=6-72+4+22=1+36=37Since AB=CASo, △ABC is an isosceles triangle
Let AD be the median through AThen D will be the mid-point of BC and coordinate of D are5+72,-2-22=6,-2Thus length of median through A=AD=6-62+(-2-4)2=0+36=6
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​Show that A(6,4), B(5,-2) and C(7,-2) are the vertices of an isosceles triangle. Also, find the length of the median through A.

Show that A(6,4), B(5,-2) and C(7,-2) are the vertices of an isosceles triangle. Also, find the length of the median through A.