Concept explainers
a.
To determine the co-ordinates of the vertex
a.
Answer to Problem 26PPS
The co-ordinate of the vertex is (4, 1).
Explanation of Solution
Given:
The vertex of the
Equations:
Calculation:
Let,
Now, Subtract equation ( ii ) from
Substituting the value of y in equation ( i ),
Conclusion:
Hence, the co-ordinate of the vertex is (4, 1).
b.
To draw the graph of the given lines and identify the vertex of the triangle
b.
Explanation of Solution
Given:
Calculation of graph:
Consider,
Values of x | Values of y |
0 | 3 |
2 | 2 |
4 | 1 |
-2 | 4 |
-4 | 5 |
Using the above table, the graph can be plotted.
Graph:
Calculation of graph:
Consider
Values of x | Values of y |
0 | 9 |
3 | 3 |
2 | 5 |
1 | 7 |
-1 | 11 |
Using the above table, the graph can be plotted.
Graph:
Plotting both the graphs on the same co-ordinate plane:
Interpretation:
From the above graph, it is clear that, the point of intersection of lines is (4, 1), which is the solution to the given equations.
Conclusion:
Hence, the vertex of the triangle is (4, 1).
c.
To draw
c.
Explanation of Solution
Given:
Calculation of graph:
Consider,
Values of x | Values of y |
0 | 3 |
2 | 2 |
4 | 1 |
-2 | 4 |
-4 | 5 |
Using the above table the graph can be plotted.
Graph:
Calculation of graph:
Consider,
Values of x | Values of y |
0 | 9 |
3 | 3 |
2 | 5 |
1 | 7 |
-1 | 11 |
Using the above table the graph can be plotted.
Graph:
Calculation of graph:
Consider,
Values of x | Values of y |
0 | 3 |
1 | 2 |
2 | 1 |
3 | 6 |
4 | 7 |
Using the above table the graph can be plotted.
Graph:
Plotting all the graphs on the same co-ordinate plane:
Interpretation:
A triangle can be seen in the graph with vertices: (0, 3), (2, 5) and (4, 1).
Conclusion:
Hence, a triangle is formed with the intersections points of the given lines.
d.
To name the other two vertices
d.
Answer to Problem 26PPS
(2, 5) and (0, 3)
Explanation of Solution
Consider the following graph from sub-part(c).
A triangle can be seen in the graph with vertices: (0, 3), (2, 5) and (4, 1).
So, the other two vertices are: (0, 3) and (2, 5).
Chapter 6 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Additional Math Textbook Solutions
Introductory and Intermediate Algebra for College Students (5th Edition)
Linear Algebra and Its Applications (5th Edition)
College Algebra (10th Edition)
Algebra and Trigonometry
College Algebra (5th Edition)
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education