Answer:
(-11,8)
Explanation:
To find the coordinates of the fourth corner of the rectangular city block, we need to use the fact that opposite sides of a rectangle are parallel and equal in length.
Let's start by finding the length of one of the sides of the rectangle. We can use the distance formula for that:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For example, if we want to find the length of the side between (2,2) and (2,-4), we have:
d = sqrt((2 - 2)^2 + (-4 - 2)^2) = sqrt(6^2) = 6
We can also see from the given coordinates that the sides of the rectangle are parallel to the x or y axis, which means that their lengths are simply the difference between the corresponding x or y coordinates.
So now we know that the length of the sides of the rectangle are both 6 units. The missing corner must be positioned 6 units away from the given point (-5,-4) along the x-axis, since the fourth side of the rectangle is parallel to the x-axis. Therefore, its x-coordinate is -5 - 6 = -11.
Similarly, the fourth corner must be positioned 6 units away from the given point (2,2) along the y-axis, since the fourth side of the rectangle is parallel to the y-axis. Therefore, its y-coordinate is 2 + 6 = 8.
Therefore, the coordinates of the fourth corner are (-11, 8).