Math Problem Statement

Find the midpoint of the segment with the following endpoints. left parenthesis, minus, 9, comma, minus, 10, right parenthesis, and , left parenthesis, 0, comma, minus, 7, right parenthesis (−9,−10) and (0,−7)

Solution

To find the midpoint of a line segment with endpoints (−9,−10)(-9, -10) and (0,−7)(0, -7), we use the midpoint formula:

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

Substitute the given coordinates:

  • x1=−9x_1 = -9, x2=0x_2 = 0
  • y1=−10y_1 = -10, y2=−7y_2 = -7

Now calculate each part:

x1+x22=−9+02=−92=−4.5\frac{x_1 + x_2}{2} = \frac{-9 + 0}{2} = \frac{-9}{2} = -4.5

y1+y22=−10+(−7)2=−172=−8.5\frac{y_1 + y_2}{2} = \frac{-10 + (-7)}{2} = \frac{-17}{2} = -8.5

Thus, the midpoint is:

(−4.5,−8.5)\boxed{(-4.5, -8.5)}

Would you like further details or have any questions?

Here are 5 related questions:

  1. How do you find the distance between two points?
  2. What is the formula for finding the slope of a line?
  3. How would you find the equation of a line passing through two given points?
  4. Can the midpoint formula be used in three-dimensional space?
  5. What is the relationship between the midpoint and the distance formula?

Tip: The midpoint is always halfway between two points on a line, making it useful for finding the center of a segment.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry

Formulas

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

Theorems

Midpoint Theorem

Suitable Grade Level

Grades 6-8

Related Recommendation

Find the Midpoint of a Segment (−9,−10) and (0,−7)

Find the Midpoint of a Line Segment with Endpoints (-9, -4) and (-5, -3)

Find the Midpoint of the Segment (9, -10) and (1, -6)

Find the Midpoint of a Segment with Endpoints (-7, -8) and (4, 7)

Find the Midpoint of a Segment: (-10, -7) and (-4, -4)