Question

What's the midpoint of a line segment joining the points (5, –4) and (–13, 12)?
Question 8 options:

A)

(–4, 4)

B)

(9, 4)

C)

(–4, 8)

D)

(4, 4)​

Answer 1

Answer:

The midpoint of the line segment is located at $\red{\bold{(-4, 4).}}$

Step-by-step explanation:

$\longrightarrow$ We're given the coordinate points of a line that can help us find the midpoint.

$\rightsquigarrow$ The midpoint formula for a line is written as:

$\bullet \ \ \ \displaystyle\big(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\big)∙$  

$\longrightarrow$ Additionally, we are given the coordinate points (5, -4) and (-13, 12). We can use these and label them with the (x, y) system so we can substitute them into the formula.

$\rightsquigarrow$ In math, a coordinate pair is written as (x, y). This is where cos = x and sin = y.

$\longrightarrow$ If we are given two coordinate pairs, we can label them with the (x, y) system but also incorporating a subscript to distinguish the two x-values from each other as well as the y-values.

$\rightsquigarrow$ We do this by turning the two x-values into x₁ and x₂ and the y-values follow the same protocol: y₁ and y₂.

$\longrightarrow$ Therefore, we can label our two coordinates:

(5, -4)

x₁ = 5

y₁ = -4

(-13, 12)

x₂ = -13

y₂ = 12

$\rightsquigarrow$ Now, we can place these values into the midpoint formula and simplify to find our midpoint.

Recall that the midpoint formula is:

$\bullet \ \ \ \displaystyle\big(\frac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\big)∙$

$\longrightarrow$ Therefore, let's substitute these values.

$\begin{gathered}\displaystyle\big \mapsto(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\big)\\\\\\\big(\dfrac{5 + (-13)}{2}, \dfrac{(-4)+12}{2}\big)\\\\\\\big(\dfrac{-8}{2}, \dfrac{8}{2}\big)\\\\\\\boxed{\blue{(-4, 4)}}\end{gathered}$

$\hookrightarrow$ Therefore, the midpoint of the line segment is located at (-4, 4), which is Option A.

Answer 2

Question

What's the midpoint of a line segment joining the points (5, –4) and (–13, 12)?

A) (–4, 4)

B) (9, 4)

C) (–4, 8)

Answer:

A) (–4, 4)

Step-by-step explanation:

• A midpoint is exactly what it sounds like; the point in the middle of two objects (in this case it's the middle of these two coordinates).
• Another way to think of the middle of something in math is by using the average.
• To find the midpoint of two points, we just find the average of the x-values and the average of the y-values:

((x1 + x2)/2 , (y1 + y2)/2)

((5 + -13) / 2 , (-4 + 12) / 2)

( -8 / 2 , 8 / 2)

(-4 , 4)