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CAT 2020 Slot 3 — QA Question 10

BasicsEasy

The points (2, 1) and (-3, -4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

Answer & solution

  • A

    15

  • B

    12

  • C

    13

  • 14

Solution

Easy

The given pair of opposite vertices forms one diagonal; the other two vertices lie on the given line, which is therefore the other diagonal. Diagonals of a parallelogram bisect each other, so the line must pass through the midpoint of the first diagonal.

1

Midpoint of the known diagonal. It joins (2,1)(2,1) and (−3,−4)(-3,-4).

M=(2+(−3)2, 1+(−4)2)⇒ M=(−0.5, −1.5)\begin{aligned} &M=\left(\frac{2+(-3)}{2},\ \frac{1+(-4)}{2}\right)\\ &\Rightarrow\ M=(-0.5,\,-1.5) \end{aligned}
2

The line passes through MM. Substitute MM into x+9y+c=0x+9y+c=0.

−0.5+9×(−1.5)+c=0⇒ −0.5−13.5+c=0⇒ c=14\begin{aligned} &-0.5+9\times(-1.5)+c=0\\ &\Rightarrow\ -0.5-13.5+c=0\\ &\Rightarrow\ c=14 \end{aligned}
c=14c=14
CAT 2020 Slot 3 QA Q10: The points (2, 1) and (-3, -4) are opposite vertices of a parallelogram. If the other two vertices lie on the — Solution | TheCATExam