Question

the coordinates of the points p,q,r are (0,4), (2,5) and (3,3) respectively. prove that triangle pqr is an isosceles right angled triangle.​

Answer 1

The distances AB and BC are " sqrt52 " and therefore isosceles."#

Explanation:

If we label them A(13,-2) B(9-8) and C(5-2)

The distance between A and B:

#13=>9=4#

#-2=>-8=6#

#4^2+6^2=52# so the distance is #sqrt52#

The distance between B and C:

#9=>5=4#

#-8=>-2=6#

#4^2+6^2=52# the distance is #sqrt52#

The distance between A and C is 8 as they are both on -2 for #y#

#color(crimson)("The distances AB and BC are " sqrt52 " and therefore isosceles."#