Answer;
x1 + k (x2-x1) , -14 + 3/8 (2-(-14))
x1 = -14, k = 3/8 and x2 =2
Thus; -14 + 3/8 (2- (-14))
Thus; the expression that correctly uses the formula to find the location of point R is;
= x1 + k (x2-x1) , -14 + 3/8 (2-(-14))
The expression correctly uses the formula to find the location of point R is [tex]\rm R = \dfrac{3}{8}(2+14)-14[/tex]
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.
The section formula is used to determine the coordinate of a point that divides a line segment joining two points into two parts such that the ratio of their length is m:n.
The given formula to find the location of point R is;
[tex]\rm \dfrac{m}{m+n}(x_2 - x_1) + x_1[/tex]
Where m is 3 and n is 5.
The number line is one-dimensional, therefore, its y-coordinate will be 0.
Therefore,
The expression is used to find the location of point R is,
[tex]\rm R= \dfrac{m}{m+n}(x_2 - x_1) + x_1\\\\R = \dfrac{3}{3+5}(2-(-14)+(-14)\\\\R = \dfrac{3}{8}(2+14)-14[/tex]
Hence, the expression correctly uses the formula to find the location of point R is [tex]\rm R = \dfrac{3}{8}(2+14)-14[/tex]
To know more about the Section formula click the link given below.
https://brainly.com/question/9316886
