Question

Segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one imolving $x$ and the other involving $y .$ Then solve for $x$ and $y .$ $$ P(2.5,1.75), M(3,2) $$

Name: Problem 72, Chapter 3: Intermediate Algebra
Uploaded: 2020-07-26T03:16:35-08:00
Duration: 1 min 31 s
Channel: Amy Jiang
Description: Segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates of the other endpoint Q . (Hint: Represent Q by (x, y) and write two equations using the midpoint formula, one imolving x and the other involving y . Then solve for x and y . P(2.5,1.75), M(3,2)

   Segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one imolving $x$ and the other involving $y .$ Then solve for $x$ and $y .$
$$
P(2.5,1.75), M(3,2)
$$

Intermediate Algebra

Margaret L. Lial,… 11th Edition

Chapter 3, Problem 72

Instant Answer

Solved by Expert Amy Jiang

07/26/2020

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We can represent the unknown endpoint Q as $(x, y)$. Show more…

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Segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one imolving $x$ and the other involving $y .$ Then solve for $x$ and $y .$ $$ P(2.5,1.75), M(3,2) $$

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Key Concepts

Midpoint Formula

The midpoint formula is a tool in coordinate geometry that calculates the midpoint of a segment by taking the average of the x-coordinates and the y-coordinates of its endpoints. This formula, expressed as ((x1 + x2)/2, (y1 + y2)/2), is essential for problems involving bisecting segments or determining central points in a coordinate plane.

Solving for an Unknown Endpoint

When one endpoint of a segment and its midpoint are known, the midpoint formula can be reversed to set up equations that determine the unknown endpoint. This involves equating the averages to the known midpoint coordinates and then solving simple linear equations for each coordinate, highlighting an application of algebra in coordinate geometry.

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