Domanda del libro di testo
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = −1, passing through (−4, − 1/4)
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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 21
Find the midpoint of each line segment with the given endpoints. (-2, -8) and (−6, −2)
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:
\(x_1 = -2, y_1 = -8\) and \(x_2 = -6, y_2 = -2\).
Substitute the values into the midpoint formula:
\[\left( \frac{-2 + (-6)}{2}, \frac{-8 + (-2)}{2} \right)\]
Simplify the expressions inside the parentheses by performing the addition in the numerators:
\[\left( \frac{-2 - 6}{2}, \frac{-8 - 2}{2} \right)\]
Calculate the final coordinates of the midpoint by dividing each sum by 2:
\[\left( \frac{-8}{2}, \frac{-10}{2} \right)\]
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Coordinate Plane and Points
The coordinate plane is a two-dimensional system where each point is identified by an ordered pair (x, y). Understanding how to plot and interpret points is essential for visualizing line segments and their properties.
Video consigliato:
05:10
Graphs & the Rectangular Coordinate System
Line Segment
A line segment is the part of a line bounded by two endpoints. Knowing the endpoints allows us to analyze properties like length and midpoint, which are fundamental in coordinate geometry.
Video consigliato:
06:49The Slope of a Line
Midpoint Formula
The midpoint formula calculates the point exactly halfway between two endpoints. It is given by ((x1 + x2)/2, (y1 + y2)/2), averaging the x-coordinates and y-coordinates separately to find the midpoint.
Video consigliato:
06:36Solving Quadratic Equations Using The Quadratic Formula
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