SOLUTION: A parallelogram whose diagonals are perpendicular is called a rhombus. Given the quadrilateral with vertices 𝐴 (−3,2),𝐵(−2,6), 𝐶(2,7),𝐷(1,3), a. Sketch the quadr

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A parallelogram whose diagonals are perpendicular is called a rhombus. Given the quadrilateral with vertices 𝐴 (−3,2),𝐵(−2,6), 𝐶(2,7),𝐷(1,3), a. Sketch the quadr      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1188582: A parallelogram whose diagonals are perpendicular is called a rhombus.
Given the quadrilateral with vertices 𝐴 (−3,2),𝐵(−2,6), 𝐶(2,7),𝐷(1,3),
a. Sketch the quadrilateral 𝐴BCD.
b. Verify that the quadrilateral ABCD is a parallelogram.
c. Verify that, in fact, it is a rhombus using the definition above.
d. Show that the rhombus can be subdivided into four right triangles.
e. Use part d. to find the area of the quadrilateral ABCD.
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!
Sunday, April 2, 2017
7:06 PM


a. You can do your own sketch.

b. A quadrilateral is a parallelogram if the opposite sides are parallel. Line segments are parallel if the lines containing them are parallel. Lines are parallel if their slopes are equal.

Slope formula:



c. Line segments are perpendicular if the slopes of the lines containing them are negative reciprocals, that is their slopes are related as follows:



d. Perpendicular lines form four right angles. A right triangle contains exactly one right angle.

e. The area of a triangle is 1/2 times the base times the altitude. In a right triangle, the two legs are the base and the altitude. Use the midpoint formulas to find the coordinates of the intersection of the two diagonals and the distance formula to find the measure of the needed line segments.

Mid-point Formulas





Distance Formula




John

My calculator said it, I believe it, that settles it

From
I > Ø