HELP I NEED THE ANSWER!!!!

Question

A(1,1) B(7,4) Find the coordinates of point C and D, as a parallelogram, rectangle, rhombus, and square. ABCD all fit together as a quadrilateral

Answer 1

With the given information, the only unique quadrilateral which can be made is a Sqaure.

Since the slope of AB is 3/6 , to find the point C (where slope of BC should be (-6/3), Starting from point B you will either go up 6 and left 3 and get (4,10) as point C and starting from point A, you will get (-2, 7) as point D doing the same thing.

or you will go down 6 and right 3, Starting from point B, to get (10, -2) as point C and starting from point A, you will get (4, -5) as point D doing the same thing.

Answer 2

It must be square with side AB = √36 + 9 = 3√5. Slope m_AB = 3/6 = 1/2. Clope of BC is - 2.

Equation of BC: y = 4 - 2(x - 7); y = - 2x + 18. Let C(x, y). Then y = - 2x + 18 and (7 - x)² + (4 + 2x - 18)² = 45;

49 - 14x + x² + 4x² - 56x + 196 - 45 = 0; 5x² - 70x + 200 = 0; x² - 14x + 40 = 0; x = 4 or x = 10

y = 10 or y = - 2. So we have 2 points C: C(4, 10) or C(10, - 2). The same , using AD we can get 2 points D.

Equation of AD: y = 1 - 2(x - 1); y = - 2x + 3; (x - 1)² + (2x - 2)² = 45; 5x² - 10x - 40 = 0;

x² - 2x - 8 = 0; x = - 2 or x = 4. So, y = 7 or y = - 5. We have 2 points D: D(- 2, 7) or D(4, - 5). We have 2 squares ABCD

Answer 3

to build a square

say D is (x4,y4) and C is (x3,y3)

say A is (x1,y1) and B is (x2,y2)

AB=r

cosθ=(x2-x1)/r

sinθ=(y2-y1)/r

then for a 90 degree rotation x4=x1-r*sinθ=x1-(y2-y1)=1--4+1=-2

y4=y1+r*cosθ=1+7-1=7

D is (-2,7)

for 90 rotation x3=x2-r*sinθ=7-4+1=4

y3=y2+r*cosθ=4+7-1=10

C is (4,10)