Question
Download Solution PDFIf P(2, 4), Q(8, 12), R(10, 14) and S(x, y) are vertices of a parallelogram, then what is (x + y) equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
O is midpoint of P and R
⇒ O = \([\frac{10+2}{2}, \frac{14+4}{2}]\) = (6,9)
Also, O is midpoint of S and Q.
⇒ O = \((\frac{x + 8}{2}, \frac{y+12}{2})\)
⇒ (6,9) = \((\frac{x + 8}{2}, \frac{y+12}{2})\)
Comparing both sides, we get
⇒ \(\frac{x+8}{2} = 6\)
⇒x =4
Also
⇒ \(\frac{y+12}{2} = 9\)
⇒ y = 6
Thus, x + y = 4 + 6 = 10
∴ Option (b) is correct
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