Question

Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M A(-3,-8) M (1,-2)

Answer 1

(5, 4)

Explanation:

`\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\$M=\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}`

Given points:

• Endpoint A = (-3, -8)
• Midpoint M = (1, -2)

Let B be the other endpoint.

Substitute the given points into the midpoint formula:

`\implies (1,-2)=\left((x_B+x_A)/(2),(y_B+y_A)/(2)\right)`

`\implies (1,-2)=\left((x_B-3)/(2),(y_B-8)/(2)\right)`

Equate the x-values to find the x-value of endpoint B:

`\implies (x_B-3)/(2)=1`

`\implies x_B-3=2`

`\implies x_B=5`

Equate the y-values to find the y-value of endpoint B:

`\implies (y_B-8)/(2)=-2`

`\implies y_B-8=-4`

`\implies y_B=4`

Therefore, the coordinates of the other endpoint are (5, 4).

Answer 2

• The other endpoint has coordinates (5, 4)

Explanation:

Each coordinate of the midpoint is the average of respective endpoints.

If (a, b) and (c, d) are endpoints, then midpoint (m, n) is:

• m = (a + c)/2 and n = (b + d)/2

Substitute the known coordinates and find the missing endpoint (x, y):

• (- 3 + x)/2 = 1 ⇒ - 3 + x = 2 ⇒ x = 3 + 2 ⇒ x = 5
• (- 8 + y)/2 = - 2 ⇒ - 8 + y = - 4 ⇒ y = 8 - 4 ⇒ y = 4

The other endpoint is (5, 4).