Geometry Problem 2
The coordinates of P, Q and R are , (1, –3) and (x, y) respectively. If R is the midpoint of PQ, find the values of x and y.
The Usual Way
Using the midpoint formula:
Hence, answer is
Estimated Time to arrive at the answer = 45 seconds.
The Smart Way
Since the y coordinate of point Q is negative with a value greater than that of point P (i.e. 3 > , the sum of these ( ) will be negative. Thus the y coordinate of the answer should be negative and the x coordinate positive. This eliminates options ‘1’, ‘2’ and ‘4’.
Now looking at the coordinates of P and Q, we observe that the ‘x’ and ‘y’ coordinates of P are fractions with denominators 3 and 2 respectively, whereas the coordinates of Q are integers.
Hence, half of the sum of ‘x’ coordinates of P and Q would yield a fraction with denominator 3 x 2 = 6.
Similarly, half of the sum of y coordinates of P and Q would yield a fraction with denominator 2 x 2 = 4.
The only option that satisfies this condition is option ‘3’.
Estimated Time to arrive at the answer = 10 seconds.
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