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In Exercises 11–26, determine whether each equation defines y as a function of x. 4x = y²
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 19
Find the midpoint of each line segment with the given endpoints. (6, 8) and (2, 4)
Guida verificata passo dopo passo1
Recall the midpoint formula for a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\):
\[\text{Midpoint} = \left( \frac{\,x_1 + x_2}{2}, \frac{\,y_1 + y_2}{2} \right)\]
Identify the coordinates of the given endpoints:
\( (x_1, y_1) = (6, 8) \) and \( (x_2, y_2) = (2, 4) \).
Substitute the values of \(x_1\), \(x_2\), \(y_1\), and \(y_2\) into the midpoint formula:
\[\left( \frac{6 + 2}{2}, \frac{8 + 4}{2} \right)\]
Simplify the expressions inside the parentheses by adding the coordinates:
\[\left( \frac{8}{2}, \frac{12}{2} \right)\]
Finally, divide each sum by 2 to find the midpoint coordinates:
\[\left( 4, 6 \right)\]
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Midpoint Formula
The midpoint formula calculates the point exactly halfway between two given points in a coordinate plane. It is found by averaging the x-coordinates and the y-coordinates of the endpoints separately: Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2). This formula helps locate the center of a line segment.
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Coordinate Plane
The coordinate plane is a two-dimensional surface defined by a horizontal x-axis and a vertical y-axis. Points are represented as ordered pairs (x, y), where x indicates horizontal position and y indicates vertical position. Understanding this system is essential for plotting points and calculating distances or midpoints.
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Line Segment
A line segment is a part of a line bounded by two distinct endpoints. Unlike a line, it has a fixed length. Knowing the endpoints of a line segment allows for calculations such as length, midpoint, and slope, which are fundamental in coordinate geometry.
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06:49The Slope of a Line
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