Skip to main content
Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 40
Chapter 3, Problem 40

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b).
midpoint (6a,6b)(6a, 6b), endpoint (3a,5b)(3a, 5b)

Verified step by step guidance
1
Recall the midpoint formula for a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\): the midpoint \((x_m, y_m)\) is given by \(x_m = \frac{x_1 + x_2}{2}\) and \(y_m = \frac{y_1 + y_2}{2}\).
Identify the known values: the midpoint is \((6a, 6b)\) and one endpoint is \((3a, 5b)\). Let the other endpoint be \((x, y)\).
Set up equations using the midpoint formula: \(6a = \frac{3a + x}{2}\) and \(6b = \frac{5b + y}{2}\).
Multiply both sides of each equation by 2 to eliminate the denominators: \(2 \times 6a = 3a + x\) and \(2 \times 6b = 5b + y\).
Solve each equation for the unknown coordinate: \(x = 2 \times 6a - 3a\) and \(y = 2 \times 6b - 5b\). These expressions give the coordinates of the other endpoint.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Midpoint Formula

The midpoint formula calculates the point exactly halfway between two endpoints of a line segment. It is found by averaging the x-coordinates and the y-coordinates of the endpoints separately, using ( (x1 + x2)/2, (y1 + y2)/2 ). This formula is essential for relating the midpoint to the endpoints.
Recommended video:
06:36
Solving Quadratic Equations Using The Quadratic Formula

Solving for an Unknown Endpoint

Given the midpoint and one endpoint, you can find the other endpoint by rearranging the midpoint formula. Multiply the midpoint coordinates by 2, then subtract the known endpoint coordinates to isolate the unknown endpoint. This method uses basic algebra to solve for missing values.
Recommended video:
Guided course
6:54
Cramer's Rule - 2 Equations with 2 Unknowns

Coordinate Geometry with Variables

When coordinates involve variables (like a and b), treat them algebraically as you would numbers. Apply the midpoint formula and algebraic operations carefully, combining like terms and solving for unknown expressions. This approach allows solving problems with symbolic coordinates.
Recommended video:
Guided course
02:16
Graphs and Coordinates - Example
Related Practice
Textbook Question

Graph each equation. 3y = x

931
views
Textbook Question

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. x2+y2-2x+12y-12=0

1053
views
Textbook Question

Give a rule for each piecewise-defined function. Also give the domain and range.

45
views
Textbook Question

Give a rule for each piecewise-defined function. Also give the domain and range.

845
views
Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. x-y<4

824
views
Textbook Question

Find the slope and y-intercept of each line, and graph it. x+2y = -4

1900
views