Question

the coordinates of endpoint D in CD are at D (5,5).if the midpoint of the segment is at M(1,_1)what are the coordinates of point C?​

Answer 1

The required points of the given line segment are ( - 3, - 7 ).

Explanation:

Given that the line segment CD whose midpoint M is ( 1, - 1 ) and point D is ( 5, 5 ), then we have to find point C of the line segment CD-

As we know that-

If a line segment AB is with endpoints (
`x_(1), y_(1)` ) and (
`x_(2), y_(2)` then the mid points C are-

C = (
`( x_(1) + x_(2) )/(2)` ,
`( y_(1) + y_(2) )/(2)` )

Here,

Let C ( x, y ), D ( 5, 5 ) with midpoint M ( 1, -1 )-

then by the midpoint formula-

( 1, -1 ) = (
`(x+ 5)/(2)` ,
`(y + 5)/(2)`

On comparing x coordinate and y coordinate -

We get,

(
`(x+ 5)/(2)` = 1 ,
`(y + 5)/(2)` = -1 )

( x + 5 = 2, y + 5 = - 2 )

( x = 2 - 5, y = -2 - 5 )

( x = - 3, y = -7 )

Hence the required points C are (- 3, - 7 ).

We can also verify by putting these points into Midpoint formula.