On a number line, the directed line segment from Q to S has endpoints Q at –8 and S at 12. Point R partitions the directed line segment from Q to S in a 4:1 ratio.Which expression correctly uses the formula to find the location of point R?

Answer: The expression that shows the location of R is, [tex]\frac{4\times 12+ 1\times -8}{4+1}[/tex]Step-by-step explanation:Since, the x-coordinate of a point on the number line shows its location.Here, the location Q and S are -8 and 12 respectively.⇒ x-coordinates of point Q and point S are -8 and 12 respectively. Q and S are lying on the number line,⇒ Coordinates of Q and S are  (-8,0) and (12,0) respectively.Now, If a point divides a line segment having end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the ratio m:nThen by the section formula,The coordinates of the point are,[tex](\frac{m\times x_2+n\times x_1}{m+n}, \frac{m\times y_2+n\times y_1}{m+n})[/tex]Here, point R partitions the directed line segment from Q to S in a 4:1 ratio.Thus, by the above formula, the coordinates of R= [tex](\frac{4\times 12+1\times -8}{4+1}, \frac{4\times 0+1\times 0}{4+1})[/tex]=  [tex](\frac{4\times 12+1\times -8}{4+1}, 0)[/tex]x-coordinate of R  =  [tex]\frac{4\times 12+1\times -8}{4+1}[/tex]⇒ Location of R =  [tex]\frac{4\times 12+1\times -8}{4+1}[/tex]Which is the required expression.