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CAT 2017 Slot 2 — QA Question 17

BasicsEasy

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

Answer & solution

Correct answer: -8

  • A

    -5

  • B

    -6

  • C

    -7

  • -8

Solution

Easy

The diagonals of a rectangle bisect each other, so both pass through the common midpoint. Find the midpoint of the given diagonal; it must satisfy the other diagonal's equation, which pins down cc.

1

Midpoint of the given diagonal. Average the endpoints (2,5)(2,5) and (6,3)(6,3).

O=(2+62, 5+32)=(4, 4)\begin{aligned} &O = \left(\tfrac{2+6}{2},\ \tfrac{5+3}{2}\right) = (4,\ 4) \end{aligned}
2

Both diagonals share this centre. So O=(4,4)O=(4,4) lies on y=3x+cy = 3x + c. Substitute.

4=3(4)+c(from step 1)⇒ 4=12+c⇒ c=−8\begin{aligned} &4 = 3(4) + c \quad\text{(from step 1)}\\ &\Rightarrow\ 4 = 12 + c\\ &\Rightarrow\ c = -8 \end{aligned}
c=−8c = -8

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CAT 2017 Slot 2 QA Q17: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the eq — Solution | TheCATExam