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The mid-point of the line segment joining $P (3 a, 4) and Q (- 3, 4 b) is (3, 4)$ . Find the value of $a and b$ .

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a = 3, b = 1

a = 3, b = 3

a = 1, b = 1

a = 1, b = 3

answer is A.

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Detailed Solution

Given points are

P (3 a, 4) and Q (- 3, 4 b)

(3, 4)

is the midpoint of

P and Q

.
We know that, if the coordinates of two points are

x 1, y 1

and

x 2, y 2

then the coordinate of the middle point of the two points will be

x 1 + x 2 2, y 1 + y 2 2

.
Then,

3 a − 3 2, 4 + 4 b 2 = (3, 4)

.
Now,

3 a − 3 2 = 3 ⇒ a = 6 + 3 3 ⇒ a = 3

Similarly,

4 + 4 b 2 = 4 ⇒ b = 8 − 4 4 ⇒ b = 1

∴ a = 3, b = 1

Hence, option (1) is correct.

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