#### Transcript of 5. The midpoints of the sides of triangle ABC are D(4,1), E(

**5. The midpoints of the sides of triangle ABC are D(4,1), E(-2,3) and F(1,-4)**

**a) Plot the midpoints. Use this plot to estimate the coordinates of the vertices of triangle ABC**

Plot the points D(4,1), E(-2,3) and F(1,-4) on the graph. After you plot the points connect them.

Now that we have ploted the midpoints and connected to points we have made a triangle.

Now find the slope of each line segment of the triangle.

So now that you have slopes you can draw the lines from each midpoint.

Heres how to do it

To find Line segment BC you must find a parallel line with it. The only parallel line is ED. So use the slope of ED (because parallel lines have same slope) and the POI of F(1,-4) to make line segment BC.

So you start at midpoint F and use the slope -1/3 and do rise over run to get line segment BC.

Do the same for finding line segments AB and AC using the slopes of DC and EF.

This is how it will look like after you draw all the line segments of triangle ABC.

Erase the lines that go outside the triangle :

Now that you have triangle ABC, you need to find the coordinates of each vertice (A,B,C). To do this you'll need to find the equation of AB, AC and BC first.

Equations of AB, AC and BC.

Now that you have the equations of each line segment , you need to use substitution method to find the coordinates for A, B and C

Here are the coordinates:

To check if we're right we can check the graph.

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