Question

On a number line, the directed line segment from Q to S has endpoints Q at a -8 and S at 12 Point R partitions the direct line segment from Q to S in a 4:1 ratio Which expression correctly uses the formula (m/m+n)(x2 - x1) + x1 to find the location of point R?

Answer 1

Answer:

$R =\frac{4}{4+1}(12 +8) -8$

Step-by-step explanation:

Given

$QS = (-8,12)$

$Ratio = 4 : 1$

Required

Determine the expression that correctly uses $\frac{m}{m+n}(x_2 - x_1) + x_1$

In $QS = (-8,12)$

$(x_1,x_2) = (-8,12)$

and

$m:n = 4:1$

Substitute these values in:

$\frac{m}{m+n}(x_2 - x_1) + x_1$

$R =\frac{4}{4+1}(12 - (-8)) + (-8)$

The expression becomes:

$R =\frac{4}{4+1}(12 +8) -8$

Solving further:

$R = \frac{4}{5}(20)-8$

$R = \frac{4*20}{5}-8$

$R = \frac{80}{5}-8$

$R = 16 - 8$

$R = 8$

Hence, R is at 8 on the number line