Write an equation of the line that contains diagonal AH.

Question

In rhombus MATH, the coordinates of the endpoints of the diagonal MT are M(0, -1) and T(4,6). Also, explain how you know your line contains diagonal AH. 

Answer 1

The property of a rhombus that you need is that the diagonals are perpendicular bisectors of each other. So this is just like the other question you wanted answered.

 

In order to write the equation of any line, you need a point that it passes through and the slope.

 

The point that it passes through in this case is the midpoint of the diagonal MT. Using the midpoint formula you get

( (0+4)/2 , (-1+6)/2 ) = (2,2.5).

 

The slope of MT is (6--1)/(4-0) = 7/4.

 

We need this because the other diagonal must be perpendicular, which means that the slopes must be negative reciprocals. So the negative reciprocal of 7/4 is -4/7.

 

Now that we have the slope and the point, we can just use y=mx+b. We have an x and y value as well as the m....so we can substitute them in and calculate b.

 

2.5 = -4/7 (2) + b

5/2 = -8/7 + b

5/2 + 8/7 = b

35/14 + 16/14 = b

51/14 = b

 

So your line has the equation y = -4/7 x + 51/14.

 

You can use this method on your other problem as well.

Hope this helped.