Question

The midpoint of AB is M(3,-4). If the coordinates of A are (7,-3), what are the coordinates of B

Answer 1

Answer: (-1,-5)

Work Shown

Let (x,y) represent the location of point B.

A = (7,-3)

B = (x, y)

Add up the x coordinates of A and B. Then divide in half to get the x coordinate of the midpoint.

(7+x)/2 = 3

7+x = 2*3

7+x = 6

x = 6-7

x = -1

This is the x coordinate of point B.

Follow similar steps for the y coordinates.

(-3+y)/2 = -4

-3+y = 2*(-4)

-3+y = -8

y = -8+3

y = -5

This is the y coordinate of point B.

Therefore, point B is located at (-1, -5)

Use the midpoint formula on points A(7,-3) and B(-1,-5) to get the midpoint M(3,-4) which will confirm the answer. I'll leave this confirmation step for the student to do.

Answer 2

B (-1, -5)

Explanation:

The midpoint formula is given by:

`\sf M = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)`

In this case, the midpoint M is (3, -4), and the coordinates of A are (7, -3).

So, let's use the formula to find the coordinates of B:

`\sf \begin{aligned} x_1 &= 7 \\ y_1 &= -3 \\ x_2 &= ? \\ y_2 &= ? \end{aligned}`

We know that the coordinates of M are (3, -4), so:

`\sf \begin{aligned} \frac{{x_1 + x_2}}{2} &= 3 \\ \frac{{7 + x_2}}{2} &= 3 \end{aligned}`

Solve for x2:

`\sf 7 + x_2 = 2 \cdot 3 \\ 7 + x_2 = 6`

Subtract 7 from both sides:

`\sf x_2 = 6 - 7 \\ x_2 = -1`

Now, for the y-coordinate:

`\sf \begin{aligned} \frac{{y_1 + y_2}}{2} &= -4 \\ \frac{{-3 + y_2}}{2} &= -4 \end{aligned}`

Solve for y2:

`\sf -3 + y_2 = 2 \cdot (-4) \\ -3 + y_2 = -8`

Add 3 to both sides:

`\sf y_2 = -8 + 3 \\ y_2 = -5`

So, the coordinates of point B are (-1, -5).