101k views
2 votes
The midpoint of

AB

is M(6,1). If the coordinates of A are (5,−4), what are the coordinates of endpoint B?

1 Answer

5 votes

Final answer:

Using the midpoint formula, the coordinates of endpoint B are found to be (7, 6) by setting up equations for both x and y coordinates based on the given midpoint M(6,1) and point A(5,−4).

Step-by-step explanation:

The midpoint formula is used to find the coordinates of the midpoint M between two points A and B on the Cartesian plane. Given that the midpoint M(6,1) is exactly halfway between points A(5,−4) and B, which we are trying to find, we can set up an equation using the midpoint formula for both x and y coordinates.

For the x-coordinate of the midpoint: (x1 + x2) / 2 = 6, where x1 is the x-coordinate of A, which is 5. We can solve for x2, which is the x-coordinate of point B. Similarly, for the y-coordinate of the midpoint: (y1 + y2) / 2 = 1, where y1 is the y-coordinate of A, which is −4. Again, solving for y2 will give us the y-coordinate of point B.

Using the midpoint formula for the x-coordinates:
(5 + x2) / 2 = 6
5 + x2 = 12
x2 = 12 − 5
x2 = 7

For the y-coordinates:

(−4 + y2) / 2 = 1
−4 + y2 = 2
y2 = 2 + 4
y2 = 6

Therefore, the coordinates of endpoint B are (7, 6).

User MaxouMask
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories