Math Problem Statement

Find of the endpoint B of BD if the midpoint C is 6,4 and the endpoint D is 11, -4

Solution

To find the coordinates of endpoint B(x1,y1)B(x_1, y_1) of line segment BDBD given that the midpoint C(6,4)C(6, 4) and the endpoint D(11,4)D(11, -4) are known, we can use the midpoint formula:

C=(x1+x22,y1+y22)C = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Here, C(6,4)C(6, 4) is the midpoint, D(11,4)D(11, -4) is the known endpoint, and B(x1,y1)B(x_1, y_1) is the endpoint we need to find.

Using the midpoint formula:

6=x1+112and4=y1426 = \frac{x_1 + 11}{2} \quad \text{and} \quad 4 = \frac{y_1 - 4}{2}

Now, solve for x1x_1 and y1y_1:

  1. For x1x_1: 6=x1+1126 = \frac{x_1 + 11}{2} Multiply both sides by 2: 12=x1+1112 = x_1 + 11 Subtract 11 from both sides: x1=1x_1 = 1

  2. For y1y_1: 4=y1424 = \frac{y_1 - 4}{2} Multiply both sides by 2: 8=y148 = y_1 - 4 Add 4 to both sides: y1=12y_1 = 12

So, the coordinates of endpoint BB are (1,12)\boxed{(1, 12)}.

Would you like to see the details or have any questions about the solution?

Here are 5 related questions you might find interesting:

  1. How do you find the midpoint between two points?
  2. What is the distance between the endpoints BB and DD of this segment?
  3. How can you verify if a point is the midpoint of a segment?
  4. What would be the coordinates of point DD if BB was at (1,12)(1, 12) and CC was at a different location?
  5. How does changing the coordinates of CC affect the location of BB if DD remains constant?

Tip: When finding endpoints using midpoints, always remember to multiply first before performing addition or subtraction.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Midpoint Formula

Formulas

Midpoint formula

Theorems

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Suitable Grade Level

Grades 9-12