Evaluate the integral. please solve with work and give final solution

The coordinates of the location of point B are (0 , 3) ⇒ answer A

Step-by-step explanation:

* Lets revise some facts

- In the square the diagonals bisect each other, that means they meet

 each other at their mid-point

- In square ABCD , AC and BD are its diagonal

- AC and DB intersect each other at point M where M is the midpoint of

 AC and BD

- The rule of the midpoint of the line whose endpoints are (x1 , y1) and

 (x2 , y2) is

∵ A = (-2 , 4) and C = (-1 , 1)

∵ M is the mid-point of AC

∴

- M is also the mid point of BD

∵ D = (-3 , 2) and M = (-1.5 , 2.5)

- Let B = (x , y)

∵ -1.5 = (x + -3)/2 ⇒ multiply both sides by 2

∴ -3 = x + - 3 add 3 to both sides

∴ 0 = x

∴ The x-coordinate of B is 0

∵ 2.5 = (y + 2)/2 ⇒ multiply both sides by 2

∴ 5 = y + 2 subtract 2 from both sides

∴ 3 = y

∴ The y-coordinate of B is 3

∴ B = (0 , 3)

* The coordinates of the location of point B are (0 , 3)