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

Answer:

2.8

Step-by-step 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:

$R=\dfrac{mx_2+nx_1}{m+n} \\=\dfrac{3(6)+2(-2)}{3+2} \\=\dfrac{18-4}{5} \\=\dfrac{14}{5} \\R=2.8$

The location of R on the number line is 2.8.

Answer 2

The answer is A. 14/5