Use the diagonals to determine whether a parallelogram with vertices A(2, 7), B(7, 9), C(5, 4), and D(0, 2) is a rectangle, rhombus, or square. Give all the names that apply.

Question

09-12-2021
Mathematics

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Use the diagonals to determine whether a parallelogram with vertices A(2, 7), B(7, 9), C(5, 4), and D(0, 2) is a rectangle, rhombus, or square. Give all the names that apply.

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reinhard10158 reinhard10158 · Answer 1 · 2021-12-09T12:31:51+01:00

Step-by-step explanation:

A and B have among each other the same distance relation as D and C : +5 in x, and +2 in y direction

and D and A have among each other the same distance relation as C and B : +2 in x, and +5 in y direction.

that means the slope of the first pair of sides is 2/5, and the slope of the second pair of sides is 5/2.

and that means that these 2 pairs of lines are not perpendicular (for this not only would we need to have the ratio upside down but also the sign would need to be flipped). there are no 90° angles.

so, there is no rectangle or square.

but because the sums of x and y coordinate differences are the same, we have the same distances between neighboring points.

and that makes it a rhombus.