Question

Point P(a/8,4) is the mid-point of the line segment joining the points A(-5, 2) and B(4, 6). The value of 'a' is(A) – 4(B) 4(C) - 8(D) – 2​

Answer 1

Answer :

The correct option is (A) -4

The value of a = -4

Given :

• The point P(a/8 , 4) is the mid point of the line joining the points A(-5 , 2) and B(4 , 6).

To Find :

• The value of a

Formula to be used :

If P(x , y) is the mid point of a line joining the points A(x₁ , yⁱ) and B(x₂ , y₂) then the coordinates are given by :

$\sf \bullet \: \: x = \dfrac{x_{2} + x_{1}}{2} \\\\ \sf \bullet \: \: y = \dfrac{y_{2} + y_{1}}{2}$

Solution :

Applying the formula for the given data :

$\sf \implies \dfrac{a}{8} = \dfrac{4+( -5)}{2} \\\\ \sf \implies a =\dfrac{(4-5)}{2}\times 8 \\\\ \sf \implies a = \dfrac{-8}{2} \\\\ \sf \implies a = -4$

Answer 2

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$\huge\tt{GIVEN:}$

• Point P(a/8,4) is the mid-point of the line segment joining the points A(-5, 2) and B(4, 6).
• The value of 'a' is(A) – 4(B) 4(C) - 8(D) – 2

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$\huge\tt{SOLUTION:}$

(If P(x , y) is the mid point of a line ,joining the points A(x₁ , yⁱ) and B(x₂ , y₂) then the coordinates would be : x = x²+x¹/2 , y = y² + y¹/2)

↪a/8 = 4+(-5)/2

↪a = 4+(-5)/2 × 8

↪a = -8 / 2

↪a = -4

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