Question

Find the following: the midpoint of (-5,0) and (4,-6).

a. (0.5, -3)
b. (-0.5, 3)
c. (2.5, -3)
d. (-2.5, 3)

Answer 1

The midpoint formula for two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\(\left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)\)

For the given points \((-5, 0)\) and \((4, -6)\), applying the midpoint formula:

\(\left(\dfrac{-5 + 4}{2}, \dfrac{0 + (-6)}{2}\right) = \left(\dfrac{-1}{2}, \dfrac{-6}{2}\right) = (-0.5, -3)\)

Therefore, the midpoint of the line segment between (-5,0) and (4,-6) is option b. (-0.5, -3).

Answer 2

The midpoint between the points (-5,0) and (4,-6) is calculated using the midpoint formula and is found to be (0.5, -3), which is option a.

Step-by-step explanation:

The correct answer is option a. To find the midpoint of the two points (-5,0) and (4,-6), you use the midpoint formula which is given by:

M = ​(​(​(x_1 + x_2)/2​), ​(​(y_1 + y_2)/2)​)​

Substitute the given points into the formula:

M = ​(​(​-5 + 4)/2​), ​(​0 - 6)/2​)​

M = ​(​(​-1)/2​), ​(-6)/2​)​

M = ​(​0.5, -3)

The correct answer is option (c) (2.5, -3).

To find the midpoint between two points, we average the x-coordinates and the y-coordinates of the given points.

For (-5,0) and (4,-6),

x-coordinate of the midpoint = (x-coordinate of the first point + x-coordinate of the second point) / 2 = (-5 + 4) / 2 = -1/2 = -0.5

y-coordinate of the midpoint = (y-coordinate of the first point + y-coordinate of the second point) / 2 = (0 + -6) / 2 = -6/2 = -3

Therefore, the midpoint is (-0.5, -3).