Question

You keep locking yourself out of your house, and your parents are getting angry. So, to encourage your memory, they are hiding a spare key in the backyard. You remember they told you they buried the key one-third of the way between the back door B(2,3) and the oak tree T(14,6). Where would the key be?

Answer 1

The location for the spare key buried one-third of the way between the back door (2,3) and the oak tree (14,6) is at coordinates (6,4).

Step-by-step explanation:

To find the location of the spare key, we can use the concept of linear interpolation between two points on a coordinate plane. The back door, B, is at point (2,3) and the oak tree, T, is at point (14,6). To find a point one-third of the way from B to T, we calculate one-third of the difference in the x-coordinates and the y-coordinates separately, then add these values to the coordinates of point B.

For the x-coordinate: one-third of the way from 2 to 14 is one-third of the difference (14 - 2 = 12), which is 4. Thus, add this to the back door's x-coordinate: 2 + 4 = 6.

For the y-coordinate: one-third of the way from 3 to 6 is one-third of the difference (6 - 3 = 3), which is 1. Thus, add this to the back door's y-coordinate: 3 + 1 = 4.

The coordinates where the spare key is buried would therefore be (6,4).