theres a diagram which in the diagram the points are: (-3,1),(0,3),(2,0),
(-1,-2).
And the directions say:
use the concept of slope to determine if the given figure is a parallelogram or a rectangle:
so this is what i did please can someone check it to see if i am correct.
M[(-3,1) to(0,3)]=(3–1)/(0-(-3)) = 2/3
M[(-1,-2)to(2,0)]=(0–(-2))/(2–(-1))= 2/3
Opposite sides are parallel, so now we test the other sides. M[(-3,1) to (-1,-2)]=(-2-1)/(-1+3)=-3/2
M [(0,3) to (2,0)]=(0–3)/(2–0) = -3 /2
Opposite sides are parallel, so we have a parallelogram.
Rectangle?
M [(-3,1)to(-1,-2)]=(-2-1)/(-1-3)= -3/2
-M or the perpendicular to the slope is 2/3
All four corners are perpendicular (forming ninety degree angles). This parallelogram is a rectangle.
correct. Inverse negative slope means perpendicular.
Just a nitpick on the question: Rectangles are parallelograms, you can check the dictionary definition of parallelogram and you will see easily that a rectangle is a parallelogram.
Your calculations and explanations are correct. By finding the slopes of the sides, you determined that opposite sides are parallel, confirming that the figure is a parallelogram. Then, by checking the slopes of the diagonals, you found that they are negative reciprocals of each other, indicating that the diagonals are perpendicular. This confirms that the parallelogram is a rectangle.
I would like to clarify one point mentioned: Yes, rectangles are a type of parallelogram. In geometry, a parallelogram is defined as a quadrilateral with opposite sides that are parallel. Since rectangles also have opposite sides that are parallel, they can be classified as parallelograms.