Math Problem Statement
If (6, −8) is the midpoint of segment PQ and the coordinates of Q are (−5, −12), find the coordinates of P
Solution
We are given that the midpoint of segment is , and the coordinates of point are . We need to find the coordinates of point .
The formula for the midpoint of a segment is: where are the coordinates of point , and are the coordinates of point .
Using the given midpoint and , we can set up the following equations:
Solving for :
Multiply both sides by 2: Add 5 to both sides:
Solving for :
Multiply both sides by 2: Add 12 to both sides:
Thus, the coordinates of point are .
Do you need further clarification or details? Here are some related questions for practice:
- What is the formula for the midpoint of a segment?
- How do you find the distance between two points?
- If and , what is the midpoint of segment ?
- What is the slope of the line passing through points and ?
- Can a line segment have a negative midpoint?
Tip: Always remember, the midpoint is simply the average of the x-coordinates and y-coordinates of the two points.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Midpoint Formula
Algebra
Formulas
Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)
Theorems
Midpoint Theorem
Suitable Grade Level
Grades 8-10
Related Recommendation
Find Coordinates of Q from Midpoint and Point P - Geometry Problem
Midpoint of a Line Segment between Two Points (-6, -1) and (-2, 5)
Find the Coordinates of Point Q Given Midpoint and Point P
Find the Midpoint of a Line Segment: P(8, 5) and Q(5, -7)
Find the Midpoint of Segment PQ with Points P=(-3,5) and Q=(1,9)