Question

If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then

the value of ‘a’ is

(a) 12

(b) -6

(c) -12

(d) -4​

Answer 1

Answer:-

Given:

(a/3 , 4) is mid point of the line segment joining the points P ( - 6 , 5) and R ( - 2 , 3).

We know that,

Mid point of a line segment joining points (x1 , y1) and (x2 , y2) is:

→ P (x , y) = [ (x₁+ x₂ )/ 2 , (y₁ + y₂ )/ 2 ]

Hence,

→ (a/3 , 4) = [ ( - 6 - 2) / 2 , (5 + 3) / 2 ]

→ (a/3 , 4) = [ - 8/2 , 8/2 ]

→ (a/3 , 4) = ( - 4 , 4)

On comparing both sides we get,

→ a/3 = - 4

→ a = ( - 4) * 3

→ a = - 12

Hence, the value of a is - 12 (Option - C).

Some Important Formulae:

• Distance between two points with coordinates ( x₁ , y₁ ) and (x₂ , y₂ ) is √[(x₂ - x₁)² + (y₂ - y₁)² ].

• Slope of a line (m) = (y₂ - y₁)/ (x₂ - x₁)

• Section formulae:

1. Internally in the ratio m : n is [ (mx₂ + nx₁) / (m + n) , (my₂ + ny₁)/(m + n) ] where m + n ≠ 0.
2. Externally is [ (mx₂ +nx₁) / (m + n) , (my₂ + ny₁)/(m + n) ] where m ≠ n.

Answer 2

Answer:

c) -12

Step-by-step explanation:

(x, y) = (x1 + x2)/2, (y1 + y2)/2

Given: x is a/3, y is 4, x1 is -6, y1 is 5, x2 is -2 and y2 is 3.

Substitute the values,

→ a/3 = (-6 + (-2))/2

→ a/3 = (-6 - 2)/2

→ a /3 = -8/2

→ a/3 = -4

→ a = - 12

Similarly,

→ 4 = (5 + 3)/2

→ 4 = 8/2

→ 4 = 4

Hence, the value of a is -12.