InterviewSolution
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InterviewSolution
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Find the area of the triangle PQR with Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2). |
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Answer» Let the co-ordinates of P and R be (a,b) and (c,d) and coordinates of Q are (3, 2) By midpoint formula. x = \(\frac{x_1+x_2}2\) , y = \(\frac{y_1+y_2}2\) (2 , - 1) is the mid-point of PQ. ∴ 2 = \(\frac{3+a}2\) and -1 = \(\frac{2+b}2\) ∴ a = 1 and b = -4 ∴ Coordinates of P are (1, -4) (1 , 2) is the mid-point of QR. ∴ 1 = \(\frac{3+c}2\) and 2 = \(\frac{2+d}2\) ∴ c = -1 and d = 2 ∴ Coordinates of P are (-1, 2) Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3) = \(\frac{1}2\) |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| Area of ∆PQR = \(\frac{1}2\) | 3( − 4 – 2 ) + 2( − 1 – 1) + 1( 2 − 4) | = \(\frac{1}2\) | − 18 − 4 − 2 | = 12 sq. units Hence the area of ∆PQR is 12 sq. units |
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