How do I find the slant and midpoint?

W

Wormman12

New member
Joined
Jan 27, 2013
Messages
15
I had this question on my final test and it was the hardest one. I got it wrong, but I would rally like an explanation:

The vertices of rectangle ABCD are A = (0, 0), B = (2a, 0), C = (2a, 2b), and D = (0, 2b). Where M, N, P, and Q are the midpoints of the consecutive sides of ABCD, what type of quadrilateral is MNPQ? Be as specific as possible.

My teacher said I should use the midpoint formula to show that they have the same midpoint and the slope formula to show slopes are opposite reciprocals, but I don't know how to set them up using a and b. Anyone able to show me? I am sure I can understand it after that.
 
Wormman12 said:
I had this question on my final test and it was the hardest one. I got it wrong, but I would rally like an explanation:

The vertices of rectangle ABCD are A = (0, 0), B = (2a, 0), C = (2a, 2b), and D = (0, 2b). Where M, N, P, and Q are the midpoints of the consecutive sides of ABCD, what type of quadrilateral is MNPQ? Be as specific as possible.

My teacher said I should use the midpoint formula to show that they have the same midpoint and the slope formula to show slopes are opposite reciprocals, but I don't know how to set them up using a and b. Anyone able to show me? I am sure I can understand it after that.
Click to expand...

What does that mean?
 
Well I know 2a and 2b means that those numbers are equidistant, from each other. so 2a=2b 2a=x, and 2b=y. this also means that C has both x and y distances. the problem is, I don't know how to set up the formula using a parralelagram.
 
Wormman12 said:
I had this question on my final test and it was the hardest one. I got it wrong, but I would rally like an explanation:

The vertices of rectangle ABCD are A = (0, 0), B = (2a, 0), C = (2a, 2b), and D = (0, 2b). Where M, N, P, and Q are the midpoints of the consecutive sides of ABCD, what type of quadrilateral is MNPQ? Be as specific as possible.

My teacher said I should use the midpoint formula to show that they have the same midpoint and the slope formula to show slopes are opposite reciprocals, but I don't know how to set them up using a and b. Anyone able to show me? I am sure I can understand it after that.
Click to expand...
Make a drawing of the rectangle, and mark the midpoints of the four sides. Halfway from A to B is (a,0). Halfway from B to C is (2a,b), etc. Also draw the lines connecting successive midpoints.

Next, notice that you have drawn a right triangle in each corner of the rectangle. What are the lengths of the sides? The hypotenuse of each right triangle?

What can you say about the slopes, in terms of a and b?
 
You must log in or register to reply here.
Top