Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Rectangle ABCD has an area of 50 units squared. If the coordinates of A are (1,2) and the coordinates of B are (5,-1), what are possible coordinates of points C and D, respectively?

A) (15,-1) and (11,2)
B) (11,7) and (7,10)
C) (5,9) and (1,12)
D) (2,-5) and (-2,-2)

Sagot :

JcAlmighty
The answer is B) (11,7) and (7,10)

First calculate the distance (d) between the points, using the formula:
d = √((y2 - y1)² + (x2 - x1)²)
A distance between points A (1,2) and B (5,-1) is:
d1 = √((-1 - 2)² + (5 - 1)²) = √((-3)² + (4)²) = √(9 + 16) = √25 = 5

So, we know that one side of the rectangle is 5 units. Using the known area of the rectangle, let's calculate the other side:
A = d1 * d2
A = 50
d1 = 5

50 = 5 * d2
d2 = 50/5
d2 = 10

We need to find slope between two points now:
m = (y2 - y1) / (x2 - x1) = (-1 - 2) / (5 - 1) = -3 / 4

Find the negative reciprocal slope:
m1 = -1/m = 4 / 3

Now, you want the points C and D 10 units (d2) away going at the slope m1:

Use the Pythagorean triple 3 : 4 : 5 to calculate sides, if hypotenuse is 10:
3 : 4 : 5 = a : b : 10
3*2 : 4*2 : 5*2 = 6 : 8 : 10

So, sides have length of 6 and 8.
Now, find possible points
A(1,2)     ⇒     D(1 + 6, 2 + 8)            or        D(1 - 6, 2 - 8)
              ⇒     D(7, 10)                       or        D(-5, -6)

B(5,-1)    ⇒     C(5 + 6, -1 + 8)            or        C(5 - 6, -1 - 8)
              ⇒     C(11,7)                          or        C(-1, -9)

Among all choices, the correct one is B) (11,7) and (7,10)
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.