Question

HELP NEEDED IN 15 mins please help meee IT WOULD MEAN ALOTTTT PLEASEEE HELP MEEEE USING ALL MY POINTS 7th grade mathhh

Which of the following points is the fourth vertex needed to create a rectangle with vertices located at (−29, 11), (−4, −2), and (−29, −2)?

(−29, −11)
(−29, 2)
(−4, 11)
(−4, 2)

Answer 1

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).