Question

Find the other endpoint of the line segment with the given endpoint and mid point 1.Endpoint: (2, 5), midpoint: (5, 1)

Answer 1

The endpoint of the line segments in each scenario are below;

1. we have: (8,-3)
2. we have: (-25,-6)
3. we have: (-1,26)
4. we have: (29,-13)
5. we have: (14,12)

From straight line geometry, it is evident that the midpoint coordinates is given as follows;

x = (x2 + x1)/2

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

Consequently, the other endpoint coordinates, x2 and y2 can be calculated as follows;

x2 = 2x - x1

x2 = 2x - x1y2 = 2y - y1

Therefore,

For Situation 1:

x2 = (2×5) - 2

x = 8

y2 = (2×1) - 5

y2 = -3.

Therefore, we have: (8,-3)

For Situation 2:

• x2 = (2×-10) - 5

x = -25

• y2 = (2×-2) - 2

y2 = -6.

Therefore, we have: (-25,-6)

For Situation 3:

• x2 = (2×4) - 9

x = -1

• y2 = (2×8) - (-10)

y2 = 26.

Therefore, we have: (-1,26)

For Situation 4:

• x2 = (2×10) - (-9)

x = 29

• y2 = (2×-3) - 7

y2 = -13.

Therefore, we have: (29,-13)

For Situation 5:

• x2 = (2×4) - (-6)

x = 14

• y2 = (2×8) - 4

y2 = 12.

Therefore, we have: (14,12)

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