Question

question 4 of 5
drag the tiles to the boxes to form correct pairs. not all tiles will be used.
the endpoints of ab are a(-7,-14) and b(5,10). into which ratio will each point divide ab?
2:1 3:1 4:3 1:2
e(1,2)
c(-3,-6)
d(2,4)

Explanation:

Step1: Recall the section formula

If a point \(P(x,y)\) 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 \(y=\frac{my_2+ny_1}{m + n}\). Here \(x_1=-7,y_1=-14,x_2 = 5,y_2=10\).

Step2: For point \(E(1,2)\)

Let the ratio be \(m:n\). Using the \(x\) - coordinate formula: \(1=\frac{5m-7n}{m + n}\). Cross - multiply: \(m + n=5m-7n\). Rearrange: \(4m = 8n\), so \(\frac{m}{n}=\frac{2}{1}\).

Step3: For point \(C(-3,-6)\)

Using the \(x\) - coordinate formula: \(-3=\frac{5m-7n}{m + n}\). Cross - multiply: \(-3(m + n)=5m-7n\). Expand: \(-3m-3n=5m-7n\). Rearrange: \(4n = 8m\), so \(\frac{m}{n}=\frac{1}{2}\).

Step4: For point \(D(2,4)\)

Using the \(x\) - coordinate formula: \(2=\frac{5m-7n}{m + n}\). Cross - multiply: \(2(m + n)=5m-7n\). Expand: \(2m+2n=5m-7n\). Rearrange: \(3m = 9n\), so \(\frac{m}{n}=\frac{3}{1}\).

Answer:

\(E(1,2)\) → \(2:1\)
\(C(-3,-6)\) → \(1:2\)
\(D(2,4)\) → \(3:1\)