Question

The midpoint of the Line Segment AB is (2, -9). The coordinates of one endpoint are A (4, 10). Find the coordinates of endpoint B.

Answer 1

B(0, -38)

Explanation:

To find the coordinates of point B, given the midpoint of line segment AB and the coordinates of point A, we can employ the following method:

1. find the translation vector from A to the midpoint
2. apply that same translation to the midpoint to get B

1. The translation vector is defined as:

`\langle x_2 - x_1, \ y_2-y_1\rangle`

for the points
`(x_1, y_1)` and
`(x_2,y_2)`.

Finding this for A(4, 10) and midpoint (2, -9):

`\langle2-4,\ -9-10\rangle`

`= \boxed{\langle-2,\ -19\rangle}`

So, the translation vector is 〈-2, -19〉.

2. Now, we can apply this to the midpoint (2, -9):

(2, -9)

+
`\langle-2,\, -19\rangle`

B(0, -38)