Question

HELP PLEASE ASAP

Answer 1

$\bold{\huge{\underline{ Solution }}}$

We have,

• Line segment AB
• The coordinates of the midpoint of line segment AB is ( -8 , 8 )
• Coordinates of one of the end point of the line segment is (-2,20)

Let the coordinates of the end point of the line segment AB be ( x1 , y1 ) and (x2 , y2)

Also,

Let the coordinates of midpoint of the line segment AB be ( x, y)

We know that,

For finding the midpoints of line segment we use formula :-

$\bold{\purple{ M( x, y) = }}{\bold{\purple{\dfrac{(x1 +x2)}{2}}}}{\bold{\purple{,}}}{\bold{\purple{\dfrac{(y1 + y2)}{2}}}}$

According to the question,

• The coordinates of midpoint and one of the end point of line segment AB are ( -8,8) and (-2,-20) .

For x coordinates :-

$\sf{ -8 = }{\sf{\dfrac{(- 2 +x2)}{2}}}$

$\sf{2}{\sf{\times{ -8 = - 2 + x2 }}}$

$\sf{ - 16 = - 2 + x2 }$

$\sf{ x2 = -16 + 2 }$

$\bold{ x2 = -14 }$

Now,

For y coordinates :-

$\sf{ 8 = }{\sf{\dfrac{(- 20 +x2)}{2}}}$

$\sf{2}{\sf{\times{ 8 = - 20 + x2 }}}$

$\sf{ 16 = - 20 + x2 }$

$\sf{ y2 = 16 + 20 }$

$\bold{ y2 = 36 }$

Thus, The coordinates of another end points of line segment AB is ( -14 , 36)

Hence, Option A is correct answer