Question

If M( 35,20) is midpoint of line AB ,and A is ( 20,10) ,find B.​

Answer 1

Answer:

B(50, 30)

Step-by-step explanation:

We've been given a line AB where A = (20, 10), and a point M(35, 20) which is the midpoint of the line AB, we're asked to find the coordinates of B.

Let B's coordinates be (x₂, y₂).

We'll be using the Midpoint Formula to find the coordinates of B.

$\sf Midpoint \ Formula \ \Longrightarrow \ M(x, y) = \Bigg\{ \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \Bigg\}$

Where M(x, y) is the midpoint, and (x₁ + x₂)/2 = x and (y₁ + y₂)/2 = y.

Using the formula we get; [x₁ = 20 & y₁ = 10]

$\sf \dashrightarrow M(35, 20) = \Bigg\{ \dfrac{20 + x_2}{2}, \dfrac{10 + y_2}{2} \Bigg\}$

Now, we'll equate (20 + x₂)/2 with 35, and (10 + y₂)/2 with 20.

Equating (20 + x₂)/2 with 35 gives;

$\sf \dashrightarrow \ 35 = \dfrac{20 + x_2}{2}$

$\sf \dashrightarrow \ 35 \times 2 = 20 + x_2$

$\sf \dashrightarrow \ 70 = 20 + x_2$

$\sf \dashrightarrow \ 70 - 20 = x_2$

$\sf \dashrightarrow \ \boxed{\sf 50 = x_2}$

Equating (10 + y₂)/2 with 20 gives;

$\sf \dashrightarrow 20 = \dfrac{10 + y_2}{2}$

$\sf \dashrightarrow 20 \times 2 = 10 + y_2$

$\sf \dashrightarrow 40 = 10 + y_2$

$\sf \dashrightarrow 40 - 10 = y_2$

$\sf \dashrightarrow \boxed{\sf 30 = y_2}$

We've got;

• x₂ = 50
• y₂ = 30

Therefore, the coordinates of B are (50, 30).