Respuesta :
Answer:
Co-ordinates of point R is (26,2)
Step-by-step explanation:
Given point:
Endpoint S(8,4)
Mid-point M of segment RS (17,3)
Let endpoint [tex]R[/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{8+x_2}{2},\frac{4+y_2}{2})[/tex]
We know [tex]M(17,3)[/tex]
So, we have
[tex](17,3)=(\frac{8+x_2}{2},\frac{4+y_2}{2})[/tex]
Solving for [tex]x_2[/tex]
[tex]\frac{8+x_2}{2}=17[/tex]
Multiplying both sides by 2.
[tex]\frac{8+x_2}{2}\times 2=17\times 2[/tex]
[tex]8+x_2=34[/tex]
Subtracting both sides by 8.
[tex]8+x_2-8=34-8[/tex]
∴ [tex]x_2=26[/tex]
Solving for [tex]y_2[/tex]
[tex]\frac{4+y_2}{2}=3[/tex]
Multiplying both sides by 2.
[tex]\frac{4+y_2}{2}\times 2=3\times 2[/tex]
[tex]4+y_2=6[/tex]
Subtracting both sides by 4.
[tex]4+y_2-4=6-4[/tex]
∴ [tex]y_2=2[/tex]
Thus co-ordinates of point R is (26,2) (Answer)
