Question

Quadrilateral ABCD has coordinates A (3, -5), B (5, -2), C (10, -4), D (8, -7). Quadrilateral ABCD is a (4 points)
Question 5 options:
1) rectangle because opposite sides are congruent and adjacent sides are perpendicular
2) square because all four sides are congruent and adjacent sides are perpendicular
3) parallelogram because opposite sides are congruent and adjacent sides are not perpendicular
4) rhombus because all four sides are congruent and adjacent sides are not perpendicular

Answer 1

http://www.wolframalpha.com/input/?i=plot++%283%2C+-5%29%2C+%285%2C+-2%29%2C+++%2810%2C+-4%29%2C+++%288%2C+-7%29

Answer 2

Find the lengths of AB, BC, CD and DA first.
Next, find the slopes of AB and BC.

Answer 3

idk how to @aum

Answer 4

Use the distance formula.
The distance between the points \((x_1,y_1), (x_2,y_2) = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
A is (3, -5), B is (5, -2). Distance AB = \(\sqrt{(5-3)^2 + (-2-(-5))^2}\)
AB = \(\sqrt{(2)^2 + (3)^2} = \sqrt{13}\)

Find BC, CD, DA

Answer 5

You need to find the slope using the points one by one, like
\[slope of line AB= (-2+5)/(5-3) = 3/2\]
similarly do for other points too.......and then find how lines are related.