Question

P(a, -3) is the midpoint of the segment joining the points R (3.b) and S (7. - 2). Find the values of a and b​

Answer 1

Question :-

P(a, -3) is the midpoint of the segment joining the points R(3, b) and S(7, -2). Find the values of a and b.

Given :-

◉ Point P(a, -3) is the midpoint of the segment joining the points R(3, b) and S(7, -2).

To Find :-

◉ Value of a and b

Solution :-

Comparing each points with the standard form of a coordinate of a two dimensional plane. we get

⇒ Point R(3, b) : x₁ = 3 , y₁ = b

⇒ Point P(a, -3) : x₂ = a , y₂ = -3

⇒ Point S(7, -2) : x₃ = 7 , y₃ = -2

Given, Point P is the midpoint of RS,

∴ Abscissa of P = (Abscissa of R + Abscissa of S) / 2

⇒ x₂ = (x₁ + x₃) / 2

⇒ a = (3 + 7)/ 2

⇒ a = 10/2

⇒ a = 5

Similarly,

⇒ Ordinate of P = (Ordinate of R + Ordinate of S)/2

⇒ y₂ = (y₁ + y₃) / 2

⇒ -3 = (b+ (-2)) / 2

⇒ -3 = (b - 2)/2

⇒ -6 = b - 2

⇒ b = -4

Hence, Value of :-

• a = 5
• b = -4

Answer 2

Step-by-step explanation:

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

Given: x is a, y is -3, x1 is 3, y1 is b, x2 is 7 and y2 is -2.

To find: value of a and b.

Substitute the values in the above mentioned formula,

→ a = (3 + 7)/2

→ a = 10/2

→ a = 5

Similarly,

→ -3 = (b + (-2))/2

→ -6 = b - 2

→ -6 + 2 = b

→ - 4 = b

Hence, the value of a is 5 and b is -4.