SOLUTION: Given: triangle ABC with vertices A(-6,-2), B(2,8), and C(6,-2). Line segment AB has midpoint E, and line segment AC has a midpoint F. Prove: ADEF is a parallelogram and ADEF is N
Algebra.Com
Question 618985: Given: triangle ABC with vertices A(-6,-2), B(2,8), and C(6,-2). Line segment AB has midpoint E, and line segment AC has a midpoint F. Prove: ADEF is a parallelogram and ADEF is NOT a rhombus.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Point D has to be at (-2,3) or (-4,-7) if indeed ADEF is a parallelogram, and it makes no difference which, the quadrilateral is not a rhombus in either case.
Use the mid-point formulas to determine the coordinates of point E and F.
and
I'll leave it to you to verify E(-2,3) and F(0,-2)
Then using the properties of a parallelogram and the fact that parallel lines have equal slopes, we can determine that point D is either (-2,3) or (-4,-7).
If ADEF were a rhombus, then either AE = EF or AF = EF (depending on where D is located)
Use the distance formula to disprove each assertion. ADEF not a rhombus, Q.E.D
Distance formula:
^2\ +\ (y_1\ -\ y_2)^2})
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
This is from the geometry regents August 2011, number 38.
Given: Triangle ABC with... (answered by KMST)
Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6),
(a)Write the equation of... (answered by D'Leeter,Edwin McCravy)
This prove is really confusing me and below have provided what i think i understand but i (answered by drk)
I need help with the following proof and CANNOT use any givens like all the angles of... (answered by richard1234)
Triangle ABC has vertices A(0,0) B(4,4) and C(0,8)
Find the equation of the line that... (answered by ikleyn)
Given points A(1,3) and B(4,-1)
An equation of line the line through G(3,-2) and... (answered by solver91311)
line segment ab has endpoints a(2 -3) and b (-4,6) what are the coordinates of the... (answered by MathLover1)
Gina wrote the following paragraph to prove that the segment joining the midpoints of two (answered by mykasha)
1.) On a number line, point A has coordinate –6, and B has coordinate 2. Which is the... (answered by Cromlix)
