Circle p is tangent to the x-axis and the y-axis. if the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.

 The length of the chord AB is √2 r units.

Step-by-step explanation: Given in the question that Circle P is tangent to the X-axis at the point A and tangent to the Y-axis at the point B.

Also, the co-ordinates of centre of the circle P are C(r, r). See the attached image below.

We are to find the length of the chord AB, with end-points A and B as the points of tangency.

From the figure, we note that

the co-ordinates of the points A and B are  (0, r) and (r, 0) respectively.

As the X-axis and Y-axis are perpendicular to each other, so the lines parallel to them, OB and OA are also perpendicular to each other.

That is, ∠ACB = 90°.

This implies that the triangle ACB is a right-angled triangle.

Now, using Pythagoras theorem in ΔACB, we have

The lengths of the line segments CA and CB are calculated, using distance formula, as follows:

From equation (i), we get

Thus, the length of the chord AB is √2 r units.

the answer is 48m^2!

step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.