Question

point a has an x coordinate of -2 and lies on a circle with a center at (0, 0) and a radius of 5. to the nearest tenth, what is the y-coordinate for point a? 4.6 4.5 4.7 4.8

Explanation:

Step1: Recall circle equation

The standard equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), where \((h,k)\) is the center and \(r\) is the radius. Here, center is \((0,0)\) and \(r = 5\), so the equation is \(x^2 + y^2 = 25\).

Step2: Substitute \(x = -2\)

Substitute \(x = -2\) into the equation: \((-2)^2 + y^2 = 25\). Simplify: \(4 + y^2 = 25\).

Step3: Solve for \(y^2\)

Subtract 4 from both sides: \(y^2 = 25 - 4 = 21\).

Step4: Solve for \(y\)

Take square root: \(y = \pm\sqrt{21}\). Calculate \(\sqrt{21} \approx 4.583\), so to nearest tenth, \(y \approx 4.6\) (since point A is in the upper half, we take the positive root).

Answer:

4.6