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

Answer:

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

Step-by-step 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 = ( $\frac{ x_{1} + x_{2} }{2}$ , $\frac{ y_{1} + y_{2} }{2}$ )

Here,

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

then by the midpoint formula-

( 1, -1 )  = ( $\frac{x+ 5}{2}$ , $\frac{y + 5}{2}$ 

On comparing x coordinate and y coordinate -

We get,

( $\frac{x+ 5}{2}$ = 1  , $\frac{y + 5}{2}$ = -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.