The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5). What is the other endpoint of the diameter?

Consider this option:
1. if the point (4;6) is the centre of the circle and the point (2;5) is the first endpoint of its diameter, then point (4;6) is the middle point of the diameter (it means that is the middle between the 1st and the 2d endpoints of diameter).
2. using the property described above:
for x of the 2d endpoint of the diameter: x=4*2-2=6;
for y of the 2d endpoint of the diameter: y=6*2-5=7.

answer: (6;7)

Answer Link

wifilethbridge wifilethbridge · Answer 2 · 2019-05-16T14:07:29+02:00

Answer:

(6,7)

Step-by-step explanation:

The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5)

Since center is the mid point of two end points of diameter .

So, we will use mid point formula

[tex](x,y)=(4,6)[/tex]

[tex](x_1,y_1)=(2,5)[/tex]

Mid point formula : [tex]x =\frac{x_1+x_2}{2}[/tex] and [tex]y =\frac{y_1+y_2}{2}[/tex]

Substitute the values

[tex]4 =\frac{2+x_2}{2}[/tex] and [tex]6 =\frac{5+y_2}{2}[/tex]

[tex]8 =2+x_2[/tex] and [tex]12 =5+y_2[/tex]

[tex]6=x_2[/tex] and [tex]7=y_2[/tex]

Thus [tex](x_2,y_2)=(6,7)/tex]

Thus the other endpoint of the diameter is (6,7)