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Mathematics

If the mid-point of the line segment joining the points P(a, b - 2) and Q(-2, 4) is R(2, -3), then the values of a and b are

  1. a = 4, b = -5

  2. a = 6, b = 8

  3. a = 6, b = -8

  4. a = -6, b = 8

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Answer

The mid-point of the line segment joining the points P(a, b - 2) and Q(-2, 4) is a+(−2)2,b−2+42\dfrac{a + (-2)}{2}, \dfrac{b - 2 + 4}{2}.

Given R(2, -3) is the mid-point.

Comparing the values of mid-point we get,

a+(−2)2=2 and b−2+42=−3\dfrac{a + (-2)}{2} = 2 \text{ and } \dfrac{b - 2 + 4}{2} = -3
⇒ a - 2 = 4 and b + 2 = -6
⇒ a = 4 + 2 and b = -6 - 2
⇒ a = 6 and b = -8.

Hence, Option 3 is the correct option.

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