Question 398171
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Hi, 
A(3,-4),B(-2,5),  and C(7,10)
{{{drawing(400,400,-10,10,-10,10,grid(1),
line(-2,5,3,-4), locate(3,-4,A), locate(-2,5,B), locate(7,10,C), 
line(3,-4,7,10), line(7,10,-2,5), graph (400,400,-10,10,-10,10))}}} 
A. Show that triangle ABC is an isosceles triangle
A(3,-4),B(-2,5),  and C(7,10)
distance AB = {{{sqrt( (5)^2 + (-9^2))}}}= distance AC = {{{sqrt(9^2 +(-2)^2 )}}}

B. Show that triangle ABC is a right triangle
 m of AB = {{{(-4-5) /( 3-(-2)) = -9/5 }}}
 m of BC = -5/-9 = 5/9
 SLOPES negative reciprocals, lines AB and BC perpendicular, &#8736;ABC = 90°