Questions: Point D is located on MV. The coordinates of D are (0,-3/4). What ratio relates MD to DV?

Transcript text: Point $D$ is located on $\overline{M V}$. The coordinates of $D$ are $\left(0,-\frac{3}{4}\right)$. What ratio relates $M D$ to $D V$ ?

Solution

Solution Steps

Step 1: Find the coordinates of M and V.

From the graph, the coordinates of point M are (-3, 2) and the coordinates of point V are (2, -2).

Step 2: Calculate the distance between M and D.

The coordinates of M are (-3, 2) and the coordinates of D are (0, -3/4). Using the distance formula: $MD = \sqrt{(0 - (-3))^2 + (-\frac{3}{4} - 2)^2}$ $MD = \sqrt{(3)^2 + (-\frac{11}{4})^2}$ $MD = \sqrt{9 + \frac{121}{16}}$ $MD = \sqrt{\frac{144 + 121}{16}}$ $MD = \sqrt{\frac{265}{16}}$ $MD = \frac{\sqrt{265}}{4}$

Step 3: Calculate the distance between D and V.

The coordinates of D are (0, -3/4) and the coordinates of V are (2, -2). Using the distance formula: $DV = \sqrt{(2 - 0)^2 + (-2 - (-\frac{3}{4}))^2}$ $DV = \sqrt{2^2 + (-\frac{5}{4})^2}$ $DV = \sqrt{4 + \frac{25}{16}}$ $DV = \sqrt{\frac{64 + 25}{16}}$ $DV = \sqrt{\frac{89}{16}}$ $DV = \frac{\sqrt{89}}{4}$

Step 4: Find the ratio MD:DV

$MD:DV = \frac{MD}{DV} = \frac{\frac{\sqrt{265}}{4}}{\frac{\sqrt{89}}{4}} = \frac{\sqrt{265}}{\sqrt{89}} = \frac{\sqrt{5*53}}{\sqrt{89}} \approx \frac{16.28}{9.38} \approx 1.74$

Counting the grids, we see MD is approximately 4 units long and DV is approximately 2 units long. So, MD:DV = 4:2 = 2:1