one endpoint of a segment is (12,-8). The midpoint is (3,18).Find the coordinates of the other endpoint

Question

help please

Answer 1

Hi Shauna,

 

12,-8 is one end, and 3,18 is the midpoint.  

(x,y)                        (x,y)

 

From one point to another, x has moved 9 units (12 to 3) and y has moved 26units (-18 to 8).  As you can observe, x is decreasing (moving leftward) and y is increasing (moving upward).  So, move another 9 units (left) on x (3-9) and 26 units (up) on y (-8-18) from (3,18) this midpoint.  You should get (-6,44) for the other endpoint.  Draw the graph (you can use ruler if you want accurate and pretty picture).

 

Good Luck.

 

To check it: use midpoint formula to calculate the midpoint (3,18).

x₁ + x₂      y₁ + y₂

     2       ,        2

 

 

12+-6    -8+44         6   36    (3,18)  It checks out!

    2     ,     2            2 ,  2  

Answer 2

coordinates of midpoint  [(x1 + x2)/2 , (y1 + y2)/2] = (3, 18)

one endpoint is (x1 , y1) = (12 , -8)

so we find (x2 , y2)

 

y-coordinate

18(2) = -8 + y2

y2 = 44

 

x-coordinate

3(2) = 12 + x2

x2 = -6

 

Therefore the other endpoint is (-6 , 44)