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Midpoint (-19,-18) endpoint (-14,-19)

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Answer:

Co-ordinates of endpoint is (-24,-17)

Explanation:

The question should be given as :

Find the coordinates of the other endpoint of the segment, given its midpoint (-19,-18) and one endpoint (-14,-19).

Step-by-step explanation:

Given point:

Endpoint (-14,-19)

Mid-point of segment (-19,-18)

Let endpoint have co-ordinates
(x_2,y_2)

Using midpoint formula:


M=((x_1+x_2)/(2),(y_1+y_2)/(2))

Where
(x_1,y_1) and
(x_2,y_2) are co-ordinates of the endpoint of the segment.

Plugging in values to find the midpoint of segment.


M=((-14+x_2)/(2),(-19+y_2)/(2))

We know
M(-19,-18)

So, we have


(-19,-18)=((-14+x_2)/(2),(-19+y_2)/(2))

Solving for
x_2


(-14+x_2)/(2)=-19

Multiplying both sides by 2.


(-14+x_2)/(2)* 2=-19* 2


-14+x_2=-38

Adding both sides by 14.


-14+x_2+14=-38+14


x_2=-24

Solving for
y_2


(-19+y_2)/(2)=-18

Multiplying both sides by 2.


(-19+y_2)/(2)* 2=-18* 2


-19+y_2=-36

Adding both sides by 19.


-19+y_2+19=-36+19


y_2=-17

Thus co-ordinates of point N is (-24,-17)

User Penta
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