Question

On a number line, the directed line segment from Q to S has endpoints Q at –2 and S at 6. Point R partitions the directed line segment from Q to S in a 3:2 ratio. Rachel uses the section formula to find the location of point R on the number line. Her work is shown below. Let m = 3, n = 2, x1 = –2, and x2 = 6. R = StartFraction m x 2 + n x 1 Over m + n EndFraction R = StartFraction 3 (6) + 2 (negative 2) Over 3 + 2 EndFraction What is the location of point R on the number line?

Answer 1

The answer is A. 14/5

Answer 2

2.8

Explanation:

R partitions the directed line segment from Q to S in a 3:2 ratio. The endpoints of Q and S are -2 and 6.

`m:n=3:2, x_1=-2, x_2=6`

Therefore, the location of point R on the number line is:

`R=(mx_2+nx_1)/(m+n) \\=(3(6)+2(-2))/(3+2) \\=(18-4)/(5) \\=(14)/(5) \\R=2.8`

The location of R on the number line is 2.8.