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

Answer:

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

Step-by-step 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

$(x,y)  =( \frac{a+c}{2} , \frac{b+d}{2} )$

Similarly, here:

$(5,2)  =( \frac{-3+x}{2} , \frac{5+y}{2} )$

⇒$5 = \frac{-3+x}{2},    2  = \frac{5+y}{2} \\\impliesc10 = -3 +x  , 4 = 5  + y\\\implies x = 10 + 3, y = 4-5$

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)