Question

show that the point (5,3) (-2,0) and (3 , -2) are the vertical of the right angle triangle and also show that midpoint of the hypotenuse is equidistant from the vertex of the triangle

Answer 1

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Answer 2

Answer:

A(5,3) , B(-2,0) , C(3,-2)

DISTANCE BETWEEN AB

==> √(5+2)²+(3-0)²

==> √(7)²+(3)²

==> √49+9

===> √58

DISTANCE B/W BC

==> √(-2-3)²+(0+2)²

==> √(-5)²+(2)²

==> √25+4

==> √29

DISTANCE BETWEEN AC

==> √(3-5)²+(-2-3)²

==> √(-2)² + (-5)²

==> √4+25

==> √29

YES , IT IS A RIGHT ANGLE TRIANGLE BECAUSE

IN THIS PYTHAGORAS THOEREM IS APPLIED

==> (AB)² = (BC)²+(AC)²

==> (√58)² = (√29)² + (√29)²

==> 58 = 29+29

==> 58 = 58

SO, IT IS A RIGHT ANGLE TRIANGLE