Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Directed line segments AC, DF, and PQ are shown on the graphs. Match each graph with the ratio in which the directed line segment is partitioned. 3 : 2 4 : 1 2 : 1 1 : 1 3 : 1 Graph shows a line segment plotted on a coordinate plane. The line segment has endpoints at A(minus 5, minus 4) and C(minus 1, 5), and it has point B at (minus 3, 1). arrowBoth Graph shows a line segment plotted on a coordinate plane. The line segment has endpoints at P(minus 4, minus 6) and R(4, minus 2), and it has point Q at (2, minus 3). arrowBoth Graph of ratio line segment on a coordinate plane. A line is represented with closed endpoint D at (minus 2, 5) in quadrant 2, and closed endpoint F at (3, minus 5) and a closed point E at (1, minus 1) in quadrant 4. arrowBoth

Answer 1

The question asks to match each graph with the ratio in which the directed line segment is partitioned. We analyze each graph using the distance formula to determine the correct ratios.

Step-by-step explanation:

The question is asking to match each graph with the ratio in which the directed line segment is partitioned. We have three graphs labeled as AC, DF, and PQ. Let's analyze each graph and determine the correct ratio:

1. Graph AC: The line segment has endpoints at A(-5, -4) and C(-1, 5), and it has point B(-3, 1). Using the distance formula, we find that AB = 2 and BC = 6. So the ratio is 2:6, which simplifies to 1:3.
2. Graph DF: The line segment has endpoints D(-2, 5) and F(3, -5), and it has a point E(1, -1). Using the distance formula, we find that DE = 7 and EF = 10. So the ratio is 7:10.
3. Graph PQ: The line segment has endpoints P(-4, -6) and R(4, -2), and it has a point Q(2, -3). Using the distance formula, we find that PQ = 10 and QR = 6. So the ratio is 10:6, which simplifies to 5:3.

Matching the ratios with the corresponding graphs, we have:

AC: 1:3
DF: 7:10
PQ: 5:3