Question

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 3:2 2:1 3:1 1:1 4:1

Explanation:

Step1: Recall partition - ratio concept

The ratio \(m:n\) of a directed line - segment divides the line - segment into \(m + n\) equal parts, where the first part has \(m\) sub - parts and the second part has \(n\) sub - parts.

Step2: Analyze the first graph (segment \(AC\))

Count the number of grid units from \(A\) to \(B\) and from \(B\) to \(C\). Suppose \(A(x_1,y_1)\), \(B(x_2,y_2)\) and \(C(x_3,y_3)\). By counting the vertical or horizontal displacements (assuming the grid is square), if we find that the displacement from \(A\) to \(B\) is \(2\) units and from \(B\) to \(C\) is \(1\) unit, the ratio of \(AB\) to \(BC\) is \(2:1\).

Step3: Analyze the second graph (segment \(DF\))

Count the number of grid units from \(D\) to \(E\) and from \(E\) to \(F\). If the displacement from \(D\) to \(E\) is \(1\) unit and from \(E\) to \(F\) is \(1\) unit, the ratio of \(DE\) to \(EF\) is \(1:1\).

Answer:

For the first graph (segment \(AC\)): \(2:1\)
For the second graph (segment \(DF\)): \(1:1\)