Question

a (2,5) and b( a,-3) are joined to get b the line ab as in the figure p (4,b) is the midpoint of ab find a and find b​

Answer 1

GIVEN :

• Point A(2,5) and B(a,-3) are joined to form a line AB
• Point P(4,b) is mid-point of line AB

To find :

• a
• b

Formula used :

For line PQ , such that P = (x₁, y₁) and Q = (x₂, y₂), midpoint R(xₘ, yₘ) is given by

$\sf \implies \: x_m \:=\: \dfrac{x_1 \:+\:x_2}{2}\\\\ \sf \implies \: y_m \:=\: \dfrac{y_1 \:+\:y_2}{2}$

Solution :

As P(4,b) is a midpoint of AB, then using midpoint formula, we get;

xₘ = 4

yₘ = b

x₁ = 2

y₁ = 5

x₂ = a

y₂ = -3

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$\sf \implies \: 4 = \dfrac{2+a}{2} \\ \\ \sf \implies \:4 \times 2 = 2 + a \\ \\ \sf \implies \:8 = 2 + a \\ \\ \sf \implies \: \: a \: = 8 - 2 \\ \\ \sf \implies \: \: \bold{a \: = \: 6}$

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$\sf \implies \:b \: = \dfrac{5 + ( - 3)}{2} \\ \\ \sf \implies \:b \: = \dfrac{5 - 3}{2} \\ \\ \sf \implies \:b \: = \dfrac{2}{2} \\ \\ \sf \implies \: \bold{b = 1}$

ANSWER :

• a = 8
• b = 1