Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
point c divides ( overline{ab} ) in a particular ratio. match point c and the ratio into which c divides ( overline{ab} ) with the endpoints of ( overline{ab} ).
point ( c(-3.6,-3.4) ) divides ( overline{ab} ) in the ratio ( 2:3 ). ( a(4,-3) ) and ( b(-7,8) )
point ( c(4,1.6) ) divides ( overline{ab} ) in the ratio ( 3:2 ). ( a(-5,2) ) and ( b(7,14) )
point ( c(3.5,-2.5) ) divides ( overline{ab} ) in the ratio ( 1:7 ). ( a(-2,-1) ) and ( b(-6,-7) )
point ( c(8,9) ) divides ( overline{ab} ) in the ratio ( 5:3 ). ( a(3,4) ) and ( b(11,12) )
point ( c(-2,5) ) divides ( overline{ab} ) in the ratio ( 2:6 ). point ( c(0,1) ) divides ( overline{ab} ) in the ratio ( 4:7 ).

Explanation:

Step1: Use the section formula

If a point \(C(x,y)\) divides the line segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\).

For \(A(4,-3)\) and \(B(-7,8)\) with ratio \(2:3\)

\(x=\frac{2\times(-7)+3\times4}{2 + 3}=\frac{-14 + 12}{5}=\frac{-2}{5}=-0.4\), \(y=\frac{2\times8+3\times(-3)}{2+3}=\frac{16-9}{5}=\frac{7}{5} = 1.4\) (Not \(C(-3.6,-3.4)\))

For \(A(-5,2)\) and \(B(7,14)\) with ratio \(3:2\)

\(x=\frac{3\times7+2\times(-5)}{3 + 2}=\frac{21-10}{5}=\frac{11}{5}=2.2\) (Not \(C(4,1.6)\))

For \(A(-2,-1)\) and \(B(-6,-7)\) with ratio \(1:7\)

\(x=\frac{1\times(-6)+7\times(-2)}{1+7}=\frac{-6 - 14}{8}=\frac{-20}{8}=-2.5\), \(y=\frac{1\times(-7)+7\times(-1)}{1 + 7}=\frac{-7-7}{8}=\frac{-14}{8}=-1.75\) (Not \(C(3.5,-2.5)\))

For \(A(3,4)\) and \(B(11,12)\) with ratio \(5:3\)

\(x=\frac{5\times11+3\times3}{5 + 3}=\frac{55 + 9}{8}=\frac{64}{8}=8\), \(y=\frac{5\times12+3\times4}{5+3}=\frac{60 + 12}{8}=\frac{72}{8}=9\)

For \(A(-2,-1)\) and \(B(-6,-7)\) with ratio \(2:6\) (simplify to \(1:3\))

\(x=\frac{1\times(-6)+3\times(-2)}{1+3}=\frac{-6-6}{4}=\frac{-12}{4}=-3\) (Not \(C(-2,5)\))

For \(A(4,-3)\) and \(B(-7,8)\) with ratio \(4:7\)

\(x=\frac{4\times(-7)+7\times4}{4 + 7}=\frac{-28+28}{11}=0\), \(y=\frac{4\times8+7\times(-3)}{4+7}=\frac{32-21}{11}=\frac{11}{11}=1\)

Answer:

• Point \(C(8,9)\) divides \(\overline{AB}\) in the ratio \(5:3\) with \(A(3,4)\) and \(B(11,12)\)
• Point \(C(0,1)\) divides \(\overline{AB}\) in the ratio \(4:7\) with \(A(4,-3)\) and \(B(-7,8)\)