Question

Find the other endpoint of a line segment with one endpoint at (-3, 5) and whose midpoint is (5, 2).

(7, 2)

Answer 1

The other end point of the segment with mid point (5,2) is (13, -1).

Explanation:

Here, let the endpoints of the segment are A (-3,5) and B (x,y)

The mid point of the segment AB is C(5,2).

Now, by MID POINT FORMULA:

If the Points P(a,b) and Q(c,d) have S(x,y) as their mid points, then

`(x,y)  =( (a+c)/(2) , (b+d)/(2) )`

Similarly, here:

`(5,2)  =( (-3+x)/(2) , (5+y)/(2) )`

⇒
`5 = (-3+x)/(2),    2  = (5+y)/(2) \\\impliesc10 = -3 +x  , 4 = 5  + y\\\implies x = 10 + 3, y = 4-5`

or, x = 13 and y = -1

⇒B(x,y) = (13,-1)

Hence the other end point of the segment with mid point (5,2)

is (x,y) = (13, -1)