Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (hint: let (x, y) be the unknown endpoint. apply the midpoint formula, and solve the two equations for x and y.)
midpoint ( -4−10), endpoint (2.−13)

The required points of the given line segment  are ( - 10, - 7 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( - 4, -10 ) and point A is ( 2, - 13), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints ( ) and  (  )then the mid points M are- 

M = ( ,  )

Here,

Let A ( 2, - 13 ), B ( x, y ) with midpoint M ( - 4, - 10 ) -

then by the midpoint formula M are-

( - 4, - 10 )  = ( , )

On comparing x coordinate and y coordinate -

We get,

( = - 4  ,   = - 10)

( x + 2 = - 8, - 13 + y = - 20 )

( x = - 8 - 2, y = - 20 + 13 )

( x = - 10, y = - 7 )

Hence the required points  A are ( - 10, - 7 ).

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

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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