Question

29. On the standard (x, y) coordinate plane, points T (1, 5) and V (13, 20) are

plotted such that TV is 3 times larger than TU. What are the coordinates of point
U?

Answer 1

To find the coordinates of point U, divide the length of TV by 3 and subtract the x-coordinate and y-coordinate of T from the x-coordinate and y-coordinate of V, respectively.

Step-by-step explanation:

To find the coordinates of point U, we first need to find the coordinates of point T and V. The x-coordinate of T is 1 and the y-coordinate is 5. The x-coordinate of V is 13 and the y-coordinate is 20.

Since TV is 3 times larger than TU, we can calculate the length of TU by dividing the length of TV by 3. The length of TV is given by the formula: √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the formula, the length of TV is √((13 - 1)^2 + (20 - 5)^2) = √(144 + 225) = √369. Thus, the length of TU is √(369/3) = √123.

To find the coordinates of U, we can subtract the x-coordinate and y-coordinate of T from the x-coordinate and y-coordinate of V, respectively. The x-coordinate of U is 13 - 1 = 12 and the y-coordinate is 20 - 5 = 15.

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