13) If AOBC is a rectangle whose three vertices are A(0,3), (0,0) and B(5,0). Then sum of the squares of its both diagonals is units,
(a) 2root34
(b) 68
(c) 34
(d) 2root68​

(b) 68

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, and . The distance between them is given by:

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

Then sum of the squares of its both diagonals is units

Both diagonals measure . Sum of squares is:

The correct answer is given by option b.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1