Answered

What are the coordinates of the midpoint of [tex]\overline{EF}[/tex] if point [tex]E[/tex] is located at [tex](-12, 5)[/tex] and point [tex]F[/tex] is located at [tex](7, -9)[/tex]?

A. [tex]\left(-\frac{5}{2}, 7\right)[/tex]
B. [tex]\left(\frac{5}{2}, 7\right)[/tex]
C. [tex]\left(-\frac{5}{2}, -2\right)[/tex]
D. [tex]\left(\frac{5}{2}, -2\right)[/tex]



Answer :

GinnyAnswer
To determine the coordinates of the midpoint of the line segment [tex]\(\overline{EF}\)[/tex] with points [tex]\(E(-12, 5)\)[/tex] and [tex]\(F(7, -9)\)[/tex], we will use the midpoint formula. The midpoint [tex]\(M\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Given the points [tex]\(E(-12, 5)\)[/tex] and [tex]\(F(7, -9)\)[/tex]:

1. Identify the coordinates of point [tex]\(E\)[/tex]: [tex]\(E = (-12, 5)\)[/tex].
2. Identify the coordinates of point [tex]\(F\)[/tex]: [tex]\(F = (7, -9)\)[/tex].

Next, apply the midpoint formula:

[tex]\[ \text{Midpoint } M = \left( \frac{-12 + 7}{2}, \frac{5 + (-9)}{2} \right) \][/tex]

Now, proceed step-by-step to find the coordinates:

1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:

[tex]\[ \frac{-12 + 7}{2} = \frac{-5}{2} = -\frac{5}{2} \][/tex]

2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:

[tex]\[ \frac{5 + (-9)}{2} = \frac{-4}{2} = -2 \][/tex]

Therefore, the coordinates of the midpoint [tex]\(M\)[/tex] are:

[tex]\[ M = \left( -\frac{5}{2}, -2 \right) \][/tex]

The correct answer is [tex]\(\left( -\frac{5}{2}, -2 \right)\)[/tex].

Other Questions