Question

What is the length of the diagonal AC in the rectangle below?

A. 10.30
B. 5
C. 9
D. 9.06

Answer 1

Firstly find the coordinates of the Point A and Point C..

Answer 2

\[\large{AC^2=AD^2+CD^2}\]

Answer 3

(-5,3) and (4,-2)

Answer 4

For A it is (-5, 3) and For C it is (4,-2)

Now apply the distance formula..

Answer 5

Find the value of AD = 3+2=5

and CD = 4 + 5 =9

Answer 6

\[\large Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Answer 7

\[\large{5^2+9^2=25+81=106=AC^2}\]
\[\large{AC=\sqrt{106}=10.29..=10.30(approx.)}\]

Answer 8

*much easier way to do* .. got it @dasDaName ?

Answer 9

so its A.

Answer 10

yes..

Answer 11

yea, i got it. ty for both

Answer 12

no problem best of luck

Answer 13

thanks again

Answer 14

The method pointed out by @waterineyes is universal for these type of problems

though here @mathslover has an easier soln

good work to both

Answer 15

\[\large Distance = \sqrt{(9)^2 + (-5)^2} = \sqrt{106} \approx 10.30\]

You can apply both you will get the same..

Answer 16

ty