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Mathematics

If the point R(5, 7) is the mid-point of the line segment joining the points P(3, y) and Q(x, 9), then (x + y) equals:

  1. 7

  2. 9

  3. 12

  4. 14

Section Formula

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Answer

Given,

R(5, 7) is the mid-point of the line segment joining the points P(3, y) and Q(x, 9).

If the point R(5, 7) is the mid-point of the line segment joining the points P(3, y) and Q(x, 9), then (x + y) equals: 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 :

⇒(5,7)=(3+x2,y+92)⇒5=3+x2 and 7=y+92⇒10=3+x and 14=y+9⇒x=7 and y=5.\Rightarrow (5, 7) = \Big(\dfrac{3 + x}{2}, \dfrac{y + 9}{2}\Big) \\[1em] \Rightarrow 5 = \dfrac{3 + x}{2} \text{ and } 7 = \dfrac{y + 9}{2} \\[1em] \Rightarrow 10 = 3 + x \text{ and } 14 = y + 9 \\[1em] \Rightarrow x = 7 \text{ and } y = 5.

x + y = 7 + 5 = 12.

Hence, Option 3 is the correct option.

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