Question

On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula to find the location of point R?

Answer 1

Answer:

$R=(\frac{3\cdot2+5\cdot(-14)}{8})$    

Step-by-step explanation:            

We have been given that on a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio.

To write the expression which will find the location of R we will use section formula when a point P divides segment internally in ratio m:n.      

$P=(\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n})$  

Now let us substitute our given values in section formula. Since number line is a one dimensional, therefore, its y-coordinate will be 0.

$R=(\frac{QR\cdot(2)+RS\cdot(-14)}{QR+RS} ,\frac{QR\cdot (0)+RS\cdot( 0)}{QR+RS})$

$R=(\frac{3\cdot(2)+5\cdot(-14)}{8} ,\frac{0}{8})$

$R=(\frac{6-70}{8} ,0)$

$R=(\frac{-64}{8} ,0)$          

$R=(-8 ,0)$      

Therefore, the expression $R=(\frac{3\times2+5\cdot(-14)}{8})$ represents the formula to find the location of point R.  

Answer 2

Answer:

A

Step-by-step explanation:

Ed2020