Question

Point A has an x-coordinate of 7 and lies below the x-axis on a circle with a center at (0, 0) and a radius of 8. To the nearest tenth, what is the y-coordinate for point A? −4.0 −3.9 −3.8 −3.7

Answer 1

the formula of a circle is: x2 + y2 = r2

substituting known values in the formula: x=7 and r=8

72 + y2 = 82

calculating for value of y:

y2=64-49

y=±√15

y=±3.9

since point A lies below the x-axis then

y=-3.9

Answer 2

Answer-

The y-coordinate for point is -3.9

Solution-

Point A has an x-coordinate of 7 and lies below the x-axis (i.e -ve y-coordinate)

Let us assume, the coordinates of the point is (7, y)

The general equation for circle with centre at (h, k) and radius r, is

$\Rightarrow (x-h)^2+(y-k)^2=r^2$

As here the centre is origin (0, 0) and radius 8, so equation of the circle is

$\Rightarrow x^2+y^2=8^2$

As point A lies on the circle, so it must satisfy the circle equation, so

$\Rightarrow 7^2+y^2=8^2$

$\Rightarrow y^2=8^2-7^2=64-49=15$

$\Rightarrow y=\pm \sqrt{15}$

As the point lies under x axis, so considering only -ve value,

$\Rightarrow y=-\sqrt{15}=-3.87\approx -3.9$