Question

Given the midpoint and one endpoint of a line segment , find the other endpoint. Endpoint: (10, 12), midpoint: (6, 9)

Answer 1

The other end-point is: (2,6)

Step-by-step explanation:

Let the end-points be:

$(x_1,y_1)\ and\ (x_2,y_2)$

(x1,y1) = (10,12)

Mid-point = M = (6,9)

The formula for mid-point is given by:

$M(x,y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Putting the values

$(6,9) = (\frac{10+x_2}{2} , \frac{12+y_2}{2})$

Putting respective coordinates equal

$6 = \frac{10+x_2}{2}\\6*2 = 10+x_2\\12 = 10+x_2\\x_2 = 12-10\\x_2 = 2\\9 = \frac{12+y_2}{2}\\9*2 = 12+y_2\\18 = 12+y_2\\y_2 = 18-12\\y_2 = 6$

The other end-point is: (2,6)

Keywords: Coordinate geometry, intercepts

Learn more about coordinate geometry at:

• brainly.com/question/833559
• brainly.com/question/8054589

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