Answer:
Co-ordinates of point N is (3,-6)
Step-by-step explanation:
Given point:
Endpoint K(7,-2)
Mid-point of segment KN (5,-4)
Let endpoint [tex]N[/tex] have co-ordinates [tex](x_2,y_2)[/tex]
Using midpoint formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are co-ordinates of the endpoint of the segment.
Plugging in values to find the midpoint of segment KN.
[tex]M=(\frac{7+x_2}{2},\frac{-2+y_2}{2})[/tex]
We know [tex]M(5,-4)[/tex]
So, we have
[tex](5,-4)=(\frac{7+x_2}{2},\frac{-2+y_2}{2})[/tex]
Solving for [tex]x_2[/tex]
[tex]\frac{7+x_2}{2}=5[/tex]
Multiplying both sides by 2.
[tex]\frac{7+x_2}{2}\times 2=5\times 2[/tex]
[tex]7+x_2=10[/tex]
Subtracting both sides by 7.
[tex]7+x_2-7=10-7[/tex]
∴ [tex]x_2=3[/tex]
Solving for [tex]y_2[/tex]
[tex]\frac{-2+y_2}{2}=-4[/tex]
Multiplying both sides by 2.
[tex]\frac{-2+y_2}{2}\times 2=-4\times 2[/tex]
[tex]-2+y_2=-8[/tex]
Adding both sides by 2.
[tex]-2+y_2+2=-8+2[/tex]
∴ [tex]y_2=-6[/tex]
Thus co-ordinates of point N is (3,-6)
