Question

13) If AOBC is a rectangle whose three vertices are A(0,3), (0,0) and B(5,0).

Answer 1

Answer:

(b) 68

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, $(x_1,y_1)$ and $(x_2,y_2)$. The distance between them is given by:

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

Diagonal:

Diagonals are a line between opposite points in a square.

In this question, it is between A(0,3) and B(5,0), and between (0,0) and (5,3). Both these diagonals have the same measure, and are the distance between these points. So

$D = \sqrt{(5-0)^2+(3-0)^2} = \sqrt{5^2 + 3^2} = \sqrt{34}$

Then sum of the squares of its both diagonals is units

Both diagonals measure $\sqrt{34}$. Sum of squares is:

$(\sqrt{34})^2 + (\sqrt{34})^2 = 34 + 34 = 68$

The correct answer is given by option b.