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Mathematics

If the point (2, 1) is the mid-point of the line segment PQ joining the points P(92,−4)P\Big(\dfrac{9}{2}, -4\Big) and Q(a, b), then (a + b) is equal to:

  1. 74\dfrac{7}{4}

  2. 114\dfrac{11}{4}

  3. 72\dfrac{7}{2}

  4. 112\dfrac{11}{2}

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Answer

Let the mid-point of PQ be (2, 1).

If the point (2, 1) is the mid-point of the line segment PQ joining the points Reflection, RSA Mathematics Solutions ICSE Class 10.

By mid-point formula,

(x, y) = (x1+x22,y1+y22)\Big(\dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

⇒(2,1)=(92+a2,−4+b2)\Rightarrow (2, 1) = \Big(\dfrac{\dfrac{9}{2} + a}{2}, \dfrac{-4 + b}{2}\Big)

Comparing the x coordinates, we get :

⇒92+a2=2⇒92+a=4⇒a=4−92⇒a=8−92=−12.\Rightarrow \dfrac{\dfrac{9}{2} + a}{2} = 2 \\[1em] \Rightarrow \dfrac{9}{2} + a = 4 \\[1em] \Rightarrow a = 4 - \dfrac{9}{2} \\[1em] \Rightarrow a = \dfrac{8 - 9}{2} = \dfrac{-1}{2}.

Comparing the y coordinates, we get :

⇒ −4+b2=1\dfrac{-4 + b}{2} = 1

⇒ -4 + b = 2

⇒ b = 6.

⇒a+b⇒−12+6⇒−1+122⇒112.\Rightarrow a + b \\[1em] \Rightarrow \dfrac{-1}{2} + 6 \\[1em] \Rightarrow \dfrac{-1 + 12}{2} \\[1em] \Rightarrow \dfrac{11}{2}.

Hence, Option 4 is the correct option.

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