# Thread: [SOLVED] Given midpoint, get vertices help!

1. ## [SOLVED] Given midpoint, get vertices help!

Hello, I need help with the following problem. Given: A (4,4), B (5,9), C (1,3) as the midpoint of the sides of triangle DEF. Find the coordinates of the vertices of triangle DEF. I've been trying to figure a solution to this problem for a good hour, and am getting frustrated. I appreciate any help I can get.

2. Originally Posted by Moncon14
Hello, I need help with the following problem. Given: A (4,4), B (5,9), C (1,3) as the midpoint of the sides of triangle DEF. Find the coordinates of the vertices of triangle DEF. I've been trying to figure a solution to this problem for a good hour, and am getting frustrated. I appreciate any help I can get.
1. Draw the triangle ABC.

2. The sides of the triangle DEF are parallel to the sides of the triangle ABC and they have to pass to one midpoint each.

3. Calculate the slopes of the sides of triangle DEF:

$\displaystyle m_{AB} = \dfrac{4-9}{4-5} = 5$

$\displaystyle m_{AC} = \dfrac{4-3}{4-1} = \dfrac13$

$\displaystyle m_{BC} = \dfrac{9-3}{5-1} = \dfrac32$

4. Determine the equations of the sides of triangle DEF:

The line passing through C is parallel to AB:

$\displaystyle y-3=5(x-1)$

The line passing through B is parallel to AC:

$\displaystyle y-9=\dfrac13(x-5)$

The line passing through A is parallel to BC:

$\displaystyle y-4=\dfrac32(x-4)$

5. Calculate the coordinates of the points of intersection between these three lines to get the ponts D, E, F.

3. Thanks a ton, it really helped!