Find all points on the x-axis of a Cartesian coordinate system that are 20 units from the point (0,12)

The point (0,12) would just be 12 points up on the y axis, so wouldn't I just count 20 spaces to the left and right so it would be (20, 12) and (-20, 12)?

Well, you're on the right track! Just be sure to remember that we're looking for points on the x-axis, which means their y-coordinate should be zero. So, while you correctly identified the points (20, 12) and (-20, 12), they don't lie on the x-axis. Can you think of the correct coordinates for the points you're looking for?

To find all points on the x-axis that are 20 units away from the point (0,12), we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, we have (x1, y1) = (0, 12) and we want to find all points on the x-axis that are 20 units away. Since any point on the x-axis has a y-coordinate of 0, we can substitute y2 = 0 into the formula:

20 = √((x2 - 0)^2 + (0 - 12)^2)

Simplifying this equation, we have:

400 = x2^2 + 144

Rearranging the equation, we have:

x2^2 = 400 - 144

x2^2 = 256

Taking the square root of both sides, we have:

x2 = ±√(256)

x2 = ±16

Therefore, the points on the x-axis that are 20 units away from the point (0,12) are (16, 0) and (-16, 0).

Thank you.

That's right.