Question

(100 points!!! I need an answer and an explanation for the answer. This is a little difficult for me so, if you could take time out of your day for an in-depth explanation, I would really appreciate it :>)

Question: If the blueprint is drawn on the coordinate plane with vertices (3, 5) and (12, 14) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning.

Answer 1

my English is bad but as far as I understand, if we moved the red point to the points that is given, could we prove the theory.

if it is, yes. the other cubes lenghts squares gatherings root means the biggest squares lenght

Answer 2

Explanation:

No, the blueprint does not accurately represent the length of the diagonal of square C.

To find the length of the diagonal, we need to use the Pythagorean Theorem, which states that for a right triangle with legs of length a and b, and hypotenuse of length c, we have:

c² = a² + b²

Since square C is a square, its sides are equal in length, so we can label the length of one side as x. Then, using the distances between the vertices of the blueprint, we can find the length of the diagonal as follows:

diagonal² = (distance between x and 14)² + (distance between x and 3)²

diagonal² = (14 - x)² + (x - 3)²

diagonal² = 196 - 28x + x² + x² - 6x + 9

diagonal² = 2x² - 34x + 205

To find the value of x that maximizes the length of the diagonal, we can take the derivative of the above expression with respect to x, set it equal to zero, and solve for x:

d/dx(diagonal²) = 4x - 34 = 0

x = 8.5

Plugging this value of x back into the expression for diagonal², we get:

diagonal² = 2(8.5)² - 34(8.5) + 205

diagonal² = 72.25

So the length of the diagonal of square C is the square root of 72.25, which is 8.5√2, or approximately 12.02.

Comparing this to the distances between the vertices in the blueprint, we can see that the distance between (3,5) and (12,14) is approximately 12.73, which is greater than the actual length of the diagonal. Therefore, the blueprint does not accurately represent the length of the diagonal of square C.