wow this is confusing!! any help?!?!?!?!?!?

Question

yeah i dont get this...
it says:
The vertices of a rectangle are A(-1, 1) B(-1,7) C(8,7) and D (8,-1)

1. what are the coordinates of E on line AB so that the area of triangle EBC is 1/4 area of ABCD?
2. find measurement of angle BCE to the nearest degree

help please and thank you?!?!?!?

yes there was a typo...im sorry the coorditates of A are (-1,-1)

Answer 1

Ok, if you first draw the rectangle out on a graph, you can see that its length is 9 and width is 6. This gives an area of 54. So the area of the triangle has to be 54/4 = 27/2 units. But the triangle has a height of 9 (ie the line BC) and its base is the length of EB, so area triangle = (base * height)/2= (EB * 9)/2 = 27/2 so EB=3 So the length of EB must be 3 units. B has y coordinate 7 so E must have y coordinate 4. It has x coordinate -1 since it lies on the line AB. So the answer to the first part is:
The coordinates of E are (-1,4)

Now the second part:

You have the length of the opposite side, BE, which is 3 units and you have the length of the adjacent side, BC, which is 9 units, so we have:

Tan BCE = 3/9, which gives the angle as 18 degrees to the nearest degree.

Hope that makes sense!

Answer 2

ABCD is not a rectangle. It is a trapezoid. Please note that CD is longer than AB. Perhaps you meant that D is D(8,+1).

Then the area of the rectangle is base * height and you get:
Area = 6*9 = 54

The area of the triangle is half the base x height. The base is BC and the height is BE.
Area = (1/2)9x = 54/4
18x = 54
x = 3

So E is three units down from B. E is E(-1,4).

2. What is the measure of < BCE?

BC = 9
BE = 3

and EBC is a right angle.

So tan BCE = BE / BC = 3/9 = 1/3
< BCE = arctan(1/3) = 18° to the nearest degree.

Answer 3

1. what are the coordinates of E on line AB so that the area of triangle EBC is 1/4 area of ABCD?

There is a problem here. For ABCD to be a rectangle y coordinate of D has to be the same as the y coordinate of A

I am going to assume that D ≡ (8,+1)

Area of Δ = ½base * height

= ½BC * h

Now if h = AB then area = ½ BC*AB

= ½ rectangle ABCD

So if AE = ½ AB

then area triangle = ½BC * h
= ½BC * AE
= ½BC * ½AB
= ¼BC*AB
= ¼ rectangle ABCD

So E is the midpoint of AB ≡ (-1, 4)

2. find measurement of angle BCE to the nearest degree

Tan = 3/9
=1/3

So
If on the other hand my assumption was wrong and in fact A ≡ (-1, -1)

a) Then E ≡ (-1, 3)

b) and tan whence

Answer 4

this is hard to explain, i'm better at doing math in my head but here goes...
1.
ok so E has to be the midpoint of AB because if you draw a diagram that would make the trianlge EBC 1/4
the midpoint formula is (y1-y2)/2 , (x1-x2)/2
(7-1)/2 , (-1+1)/2
3 , 0 = the midpoint of AB (E)
2.
ok this part confused me since i didn't have graph paper, and I did it in my head, but I'm pretty sure the angle is 45 since the triangle is 1/4 of the rectangle... and from knowing geometry I'm pretty sure that is the answer.

Answer 5

.

a)y coordinate of E=-1+((3/4)(7--1)) = -1+(6) = 5 So E=(-1,5)

b)Okay angle BCE = arctan((7-5)/(8--1)) = arctan(2/9) =12.5288 degrees approximately.

Answer 6

First, the length of AB of 6.
The length of BC is 9.
So, what we're trying to get here is (1/4)(6)9=1/2(9)(h)
1/4(54)=9/2h
27/2=9/2h
h=3
7-3=4
E(-1,4)

I don't know how to do 2. I hope this helped.

Answer 7

are the coordinates od D are (8,-1) or (8,1)