Question

point s lies on qr such that qs:rs is 4:3. graph s.

Explanation:

Step1: Find coordinates of Q and R

Let's assume Q is at (11, 1) and R is at (4, 15).

Step2: Use section - formula

The section - formula for a point \(S(x,y)\) that divides the line - segment joining \(Q(x_1,y_1)\) and \(R(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(m = 4\) and \(n = 3\), \(x_1=11,y_1 = 1,x_2=4,y_2=15\).
\[x=\frac{4\times4+3\times11}{4 + 3}=\frac{16 + 33}{7}=\frac{49}{7}=7\]
\[y=\frac{4\times15+3\times1}{4 + 3}=\frac{60+3}{7}=\frac{63}{7}=9\]

Answer:

The point \(S\) is at \((7,9)\). Plot the point \((7,9)\) on the graph.