The hypotenuse of a right angled triangle has its ends at the points ((1, 3)) and (-4, 1). Find the equation of the legs of the triangle?

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Answer 1 · 2018-04-20T12:05:26

The equation of legs are #x=1, y=1# or # x=-4, y=3#

The legs in a right angled triangle are perpendicular to each other.

The ends of hypotenuse are # (1,3 ) and (-4,1)# , so other point

of the triangle is either #(1,1) or (-4,3)# . Let it be # (1,1)#

The leg joining # (1,1) and (1,3)# is perpendicular line , which is

parallel to the y-axis . So equation of the leg joining

# (1,1) and (1,3)# is #x=1#. The leg joining # (-4,1) and (1,1)# is

base , which is parallel to the x-axis . So equation of the leg

joining # (-4,1) and (1,1)# is #y=1.#The equation of legs are

#x=1, y=1# Similarly for point #(-4,3)# the equation of legs are

#x=-4, y=3# [Ans]