Question

Points S(1,18), T(16,13), and U(x, y) are collinear. T divides SU such that ST:TU is 5:U. What is the value of x?

a) 8
b) 10
c) 12
d) 14

Answer 1

The value of x in the collinear points problem is 31.

Step-by-step explanation:

First, we need to find the coordinates of point U. From the given information, we know that the ratio ST:TU is 5:U. This means that the distance from S to T is 5 times the distance from T to U.

Using the distance formula, we can find the distance between S and T as follows:

ST = sqrt((16 - 1)^2 + (13 - 18)^2) = sqrt(225) = 15

Since ST:TU is 5:U, we can set up the following proportion:

5/U = 15/TU

Cross-multiplying gives us:

5 * TU = 15 * U

Dividing both sides by 5 gives us:

TU = 3U

Substituting the coordinates of points T and U into the proportion, we get:

(16 - x)/(13 - y) = 3U/U

Substituting the coordinates of point S into the equation, we can solve for x:

(16 - x)/(13 - 18) = 3

16 - x = 3(13 - 18)

16 - x = 3(-5)

x = 16 + 15

x = 31

Therefore, the value of x is 31.