Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.
directed line segments ac, df, and pr are shown on the graphs. match each graph with the ratio in which the directed line segment is partitioned.
4:1 1:1 3:2 2:1 3:1

Explanation:

Step 1: Analyze \(PR\)

Let \(P(-5,-4)\) and \(R(4,-2)\). Assume the point \(Q\) divides \(PR\) in the ratio \(m:n\). Using the section formula for \(x\) - coordinate \(x=\frac{mx_2+nx_1}{m + n}\). Let \(Q(x,y)\) where \(x = 1,y=-3\). For \(x\) - coordinate: \(1=\frac{m\times4+n\times(-5)}{m + n}\), \(m + n=4m-5n\), \(3m = 6n\), \(m:n = 2:1\).

Step 2: Analyze \(AC\)

Let \(A(-4,-4)\) and \(C(-1,6)\). Assume the point \(B\) divides \(AC\) in the ratio \(m:n\). Using the section formula for \(y\) - coordinate \(y=\frac{my_2+ny_1}{m + n}\). Let \(B(x,y)\) where \(x=-2,y = 1\). For \(y\) - coordinate: \(1=\frac{m\times6+n\times(-4)}{m + n}\), \(m + n=6m-4n\), \(5m=5n\), \(m:n = 1:1\).

Answer:

\(PR:2:1\), \(AC:1:1\)