Question

A rectangle is a quadrilateral with four right angles and congruent diagonals. To prove that the points A(-4, 52), B(3, 92), C(4, 1), D(-3, -1) graphed on the coordinate plane form a rectangle, Janet calculated the diagonals of the quadrilateral in order to show congruence. What is the length of diagonal AC?

Select one:
A. √2474
B. 8.0
C. √66
D. √2654

Answer 1

Answer:

D. $\sqrt {2665}$

Step-by-step explanation:

We have been given the points A (-4, 52), B (3, 92), C (4, 1) and D (-3, -1).

Length of the diagonal AC can be calculated from the distance between two points formula or we can also use Pythagoras theorem to calculate the length of the diagonal. But to calculate the length of the diagonal from pythagoras theorem we need to calculate the length of the sides AB and BC, therefore, we will use distance formula to calculate the length of diagonal AC, directly.

Co-ordinates of point A is (-4, 52) and C is (4, 1), using the distance formula we get,

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

$d=\sqrt{(1-52)^2+(4-(-4))^2}$

$d=\sqrt{8^2+(-51)^2}$

$d= \sqrt{64+2601}$

$d=\sqrt{2665}$

Therefore, the length of diagonal AC is $\sqrt{2665}$, the closest option is option D.