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The mid-point of the line segment joining A(p, 5) and B(3, q) is M(-1, 4). Find the values of p and q.

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Given,

Mid-point of the line segment joining A(p, 5) and B(3, q) is M(-1, 4).

The mid-point of the line segment joining A(p, 5) and B(3, q) is M(-1, 4). Find the values of p and q. Reflection, RSA Mathematics Solutions ICSE Class 10.

By using mid-point formula,

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

Substituting values we get :

⇒(−1,4)=(p+32,5+q2)⇒(−1,4)=(p+32,5+q2)⇒−1=p+32 and 4=5+q2⇒p+3=−2 and 5+q=8⇒p=−2−3 and q=8−5⇒p=−5 and q=3.\Rightarrow (-1, 4) = \Big(\dfrac{p + 3}{2}, \dfrac{5 + q}{2} \Big) \\[1em] \Rightarrow (-1, 4) = \Big(\dfrac{p + 3}{2}, \dfrac{5 + q}{2}\Big) \\[1em] \Rightarrow -1 = \dfrac{p + 3}{2} \text{ and } 4 = \dfrac{5 + q}{2} \\[1em] \Rightarrow p + 3 = -2 \text{ and } 5 + q = 8 \\[1em] \Rightarrow p = -2 - 3 \text{ and } q = 8 - 5 \\[1em] \Rightarrow p = -5 \text{ and } q = 3.

Hence, p = -5 and q = 3.

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