SOLUTION: Please help! Verify that the points (0, 0) and (a, 0) and (a/2,a/2) form the vertices of a right triangle. Work in terms of a.

Question 65136: Please help! Verify that the points (0, 0) and (a, 0) and (a/2,a/2) form the vertices of a right triangle. Work in terms of a.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Please help! Verify that the points P=(0, 0) and Q=(a, 0) and R=(a/2,a/2) form the vertices of a right triangle. Work in terms of a.
PQ^2=A^2
QR^2=[A-(A/2)]^2+(A/2)^2= A^2/4 + A^2/4 = A^2/2
PR^2=(A/2)^2+(A/2)^2=A^2/4 + A^2/4 = A^2/2
HECE PQ^2=A^2=QR^2+PR^2=A^2/2 + A^2/2
HENCE PQR IS A RIGHT ANGLED TRIANGLE AT R.

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