Question

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

Answer 1

Answer:

The midpoint of the line segment is located at (-4, 4).

Step-by-step explanation:

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

The midpoint formula for a line is written as:

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

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.

In math, a coordinate pair is written as (x, y). This is where cos = x and sin = y. 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. We do this by turning the two x-values into x₁ and x₂ and the y-values follow the same protocol: y₁ and y₂.

Therefore, we can label our two coordinates:

(5, -4)

• x₁ = 5
• y₁ = -4

(-13, 12)

• x₂ = -13
• y₂ = 12

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

Recall that the midpoint formula is:

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

Therefore, let's substitute these values.

$\displaystyle\big(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\big)\\\\\\\big(\frac{5 + (-13)}{2}, \frac{(-4)+12}{2}\big)\\\\\\\big(\frac{-8}{2}, \frac{8}{2}\big)\\\\\\\boxed{(-4, 4)}$

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

Answer 2

Answer: Great question! 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)

So the answer would be A)

(-4, 4)

Explanation:

let ( x,y) be the midpoint of the line segment, then x =  5+(-13) / 2 = -8/2 = -4 and y = -4+(12 ) / 2 = 8/2 = 4, the mid point is ( -4,4)