Question

If R(-2,-1) is the midpoint of ST and S(-14,3),find the coordinates of t

Answer 1

Answer

Explanation

Mathematically, if a point R(x, y) divides the coordinates S (x₁, y₁) and T (x₂, y₂) internally in the ratio m:n then point R(x, y) is given as

x = [(mx₂ + nx₁)/(m + n)]

y = [(my₂ + ny₁)/(m + n)]

For this question, we are given that

R (x, y) = R(-2, -1)

S (x₁, y₁) = S (-14, 3)

T (x₂, y₂) = ?

Since it is divided equally into two parts (As per the midpoint), m : n = 1 : 1

x = -2

y = -1

x₁ = -14

y₁ = 3

x₂ = ?

y₂ = ?

m = 1

n = 1

x = [(mx₂ + nx₁)/(m + n)]

-2 = [(1 × x₂) + (1 × -14)]/(1 + 1)

-2 = [x₂ - 14]/2

$\begin{gathered} -2=\frac{x_{2}-14}{2} \\ \text{Cross multiply} \\ x_{2}-14=2\times-2 \\ x_{2}-14=-4 \\ x_{2}=-4+14 \\ x_{2}=10 \end{gathered}$

y = [(my₂ + ny₁)/(m + n)]

-1 = {