Question

The coordinates of triangle XYZ are X (-3, 3.3), Y (-3, -5.2), and Z (4.5, -5.2). Give the coordinates for two points that are five units from point Z.

Answer 1

The two points that are five units from point Z (4.5, -5.2) are points A (9.5, -5.2) and B (-0.5, -5.2).

Step-by-step explanation:

To find two points that are exactly five units away from point Z (4.5, -5.2), we are essentially looking for points on a circle with a radius of 5 units centered on Z in the Cartesian plane.

We can use the formula for a circle which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

For our circle, h = 4.5 and k = -5.2, and r = 5 units.

Because we are asked for only two points, and there are infinitely many points on the circumference, we can choose two points by considering horizontal or vertical positions from Z.

For example, moving horizontally 5 units to the right will give us point A (9.5, -5.2), and moving 5 units to the left will give us point B (-0.5, -5.2).

These are just two of the infinite points that are 5 units from point Z.