Answer:
Explanation:
To create a rectangle, we need to find a point that is the same distance from (-29, 11) as it is from (-4, -2).
First, let's find the midpoint of the line segment connecting (-29, 11) and (-4, -2):
Midpoint = ((-29 + (-4))/2, (11 + (-2))/2) = (-33/2, 9/2)
This midpoint is equidistant from (-29, 11) and (-4, -2). To find the fourth vertex of the rectangle, we need to find a point that is also equidistant from (-29, -2) and the midpoint.
The x-coordinate of this point must be -29, so we only need to find the y-coordinate:
distance from (-29, -2) to midpoint = distance from (x, y) to midpoint
sqrt[(-33/2 - (-29))^2 + (y - 9/2)^2] = sqrt[(-4 - (-29))^2 + (-2 - 11)^2]
Simplifying the equation, we get:
sqrt[(5/2)^2 + (y - 9/2)^2] = sqrt[25 + 169]
(5/2)^2 + (y - 9/2)^2 = 194
Simplifying further, we get:
(y - 9/2)^2 = 179/4
y - 9/2 = +/- sqrt(179)/2
y = 9/2 +/- sqrt(179)/2
Since (-29, -2) has a lower y-coordinate than the midpoint (-33/2, 9/2), we must choose the negative square root:
y = 9/2 - sqrt(179)/2
Therefore, the fourth vertex needed to create a rectangle is (-29, 2).
So the answer is (B) (-29, 2).