SOLUTION: My daughter needs help on an extra credit question and I have never taken Algebra. Could someone please help us?? It's a three part question 1.Given: K(0, 4), A(3, 6), T(6, 2),

Question 939575: My daughter needs help on an extra credit question and I have never taken Algebra. Could someone please help us?? It's a three part question
1.Given: K(0, 4), A(3, 6), T(6, 2), E(0, -2)
Prove: KATE is a trapezoid
Please use slope formula and show all work(plug and chug)
2. Given: A (-3, 2), B (-2, 6), C (2, 7), D (1, 3)
Prove: ABCD is a rhombus
Please use slope formula and show all work (plug and chug)
3. Write a concluding sentence stating what you have proved and why it is true
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.Given: K(0, 4), A(3, 6), T(6, 2), E(0, -2)
Prove: KATE is a trapezoid
Plot and connect the points in such a way that they form a trapezoid.
You should see KA is parallel to ET
---
Check the slopes of KA and ET
slope of KA = (6-4)(3-0) = 2/3
slope of ET = (-2-2)/(0-6) = -4/-6 = 2/3
--------------------------------------
Therefore DA is parallel to ET.
Since KATE is a quadrilateral and one pair of opposite
sides are parallel, KATE is a trapezoid.
------

Please use slope formula and show all work(plug and chug)
2. Given: A (-3, 2), B (-2, 6), C (2, 7), D (1, 3)
Prove: ABCD is a rhombus
Plot the points and connect them so you can see that ABCD is a rhombus.
Show that AB = BC = CD = EA
AB = sqrt[(-2--3)^2+(6-2)^2] = sqrt[1+16] = sqrt(17)
-----------------------
BC = sqrt[(7-6)^2+(2--2)^2] = sqrt(1 + 16) = sqrt(17)
etc. for CD and KA
======
Since all sides are equal ABCD is a rhombus.
----------
Cheers
Stan H.
---------------
Please use slope formula and show all work (plug and chug)
You could check the slopes also, but it is not a necessary condition.
----------------
3. Write a concluding sentence stating what you have proved and why it is true
Done above.

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