Math Problem Statement

B is the midpoint of AC and E is the midpoint of BD. If A(-9,-4), C(-1,6), and D(-3,-7), find the coordinates of B and E.

Solution

The problem asks us to find the coordinates of points BB and EE, where:

  • BB is the midpoint of ACAC,
  • EE is the midpoint of BDBD.

We are given the coordinates of the points:

  • A(−9,−4)A(-9, -4),
  • C(−1,6)C(-1, 6),
  • D(−3,−7)D(-3, -7).

Step 1: Finding BB (midpoint of ACAC)

The formula for the midpoint between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

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

For BB (midpoint of ACAC):

= \left( \frac{-10}{2}, \frac{2}{2} \right) = (-5, 1)$$ ### Step 2: Finding $$E$$ (midpoint of $$BD$$) Now, we use the midpoint formula again for $$B(-5, 1)$$ and $$D(-3, -7)$$: $$E = \left( \frac{-5 + (-3)}{2}, \frac{1 + (-7)}{2} \right) = \left( \frac{-8}{2}, \frac{-6}{2} \right) = (-4, -3)$$ ### Final Answer: - The coordinates of $$B$$ are $$(-5, 1)$$, - The coordinates of $$E$$ are $$(-4, -3)$$. Let me know if you'd like further details or have any other questions! Here are five related questions: 1. How do you find the midpoint of two points in 3D space? 2. What are the properties of a line segment's midpoint in geometry? 3

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Midpoints

Formulas

Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)

Theorems

Midpoint theorem

Suitable Grade Level

Grades 8-10

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