## Trending News

# the quadrilateral ABCD and has three verticies: A(0,0) B(3,4) C(8,4)?

how do you find the forth vertex for D, for

a) rhombus

b) isosceles trapezoid

c)kite

### 4 Answers

- Charles DLv 69 years agoFavorite Answer
sketch the three point on graph paper.

A is at the origin, B and C are on the line y = 4.

A rhomus has all 4 sides equal. See first refernce below.

So the length of the top line (going from B to C) must be the same length as the line going from the origin out to the right. The length of B C is 8 - 3 = 5 . So the point to the right of the origin must be 5 over from (0, 0) so ==> (5, 0)

An isosceles trapezoid has a slant up a flat top and a slant down. The slant up and down are mirror images of each other (see second reference)

So the distance directly below the point C to the end of the trapezoid must be the same as the distance directly below B to the orgin. This is 3. So D is 8 + 3 = 11 So ==> (11,0)

For a Kite the distance from the A to B and A to D must be the same and

The distance from C to B and C to D must be the same.

We already have this with the rhombus. All sides have a length of 5. So D = (5,0)

Hope this helps.

Source(s): http://www.mathsisfun.com/definitions/rhombus.html http://en.wikipedia.org/wiki/Isosceles_trapezoid http://en.wikipedia.org/wiki/Kite_(geometry) - Ossi GLv 79 years ago
Hello

AB = √(3^2+4^2) = 5 and BC = 5

--> AB = BC = 5

a) slope of AC = 4/8

slope of BD is then - 8/4

line BD is

y = -2x + b put in B

4 = -2*3 + b --> b = 10

y = -2x + 10

find intersection point E with AC

-2x + 10 = x/2

10 = 5/2*x

x = 4

y = 2

vector BE = E-B = (1, -2)

double BE = (2, -4)

add double BE to B

D = (3, 4) + (2, -4) = (5, 0) <--- ans.

b) add horizontal distance AB to horizontal distance of C:

D = (11, 0)

c) any point on the line

y = -2x + 10

e.g., set x = 10, --> y = - 10

D = (10, -10) or (8, - 6)

Regards

- justaguyLv 69 years ago
plot the points and use the properties of the objects to predict where teh last vertex is

a rhombus has all congruent sides. in your example, the sides are 5 units long. which point is 5 units from the two other corners

- masriLv 44 years ago
That became large! You get a large call. i will provide you with my 3 short bar jokes: A mushroom walks right into a bar. The bartender says, "we do not serve your form!" The mushroom asks, "Why no longer? i'm a exciting guy (fungi) Jumper cables walk right into a bar & ask in the journey that they are oftentimes served. The bartender says, "confident, ....do exactly not initiate something!!" A sandwich walks right into a bar. The bartender says, "i'm sorry....we do not serve nutrients the following!"