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
b) isosceles trapezoid
- 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
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)
- 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
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