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Magazine Chapter 2: Problem 2
Plot the points \(A(-3,1), B(3,1), C(-2,-3), D(0,3),\) and \(E(2,-3)\) on a coordinate plane. Draw the line segments \(A B, B C, C D, D E,\) and \(E A\)
Short Answer
Expert verified
Draw the points and connect them in the listed order to form a shape.
Step by step solution
01
Plot Points on Coordinate Plane
Begin by plotting each point on the coordinate plane. Locate the x-coordinate first, and then move vertically to the y-coordinate. Mark these points:
- Point A at (-3, 1)
- Point B at (3, 1)
- Point C at (-2, -3)
- Point D at (0, 3)
- Point E at (2, -3).
02
Draw Line Segment AB
Draw a straight line connecting the points A (-3, 1) and B (3, 1) on the coordinate plane. This will form a horizontal line.
03
Draw Line Segment BC
Connect point B (3, 1) to point C (-2, -3) with a straight line. This line will have a negative slope.
04
Draw Line Segment CD
Now draw a line from point C (-2, -3) to point D (0, 3). This line will have a positive slope.
05
Draw Line Segment DE
Connect point D (0, 3) to point E (2, -3) with a straight line. This line will also have a negative slope.
06
Draw Line Segment EA
Finally, connect point E (2, -3) back to point A (-3, 1) to complete the shape. This line will have a positive slope.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Plotting Points
Plotting points on a coordinate plane is a fundamental concept in coordinate geometry.
To plot a point, you need two numbers known as coordinates.
The first number is the x-coordinate and the second is the y-coordinate.
Start by locating the x-coordinate on the horizontal axis (x-axis).
Then move vertically to find the y-coordinate on the vertical axis (y-axis).
- Point A at (-3, 1) means you move 3 units left along the x-axis, then 1 unit up.
- Point B at (3, 1) means you move 3 units right along the x-axis, then 1 unit up.
- Point C at (-2, -3) means you move 2 units left along the x-axis, then 3 units down.
- Point D at (0, 3) means you stay on the origin for the x-axis, then move 3 units up.
- Point E at (2, -3) means you move 2 units right along the x-axis, then 3 units down.
Line Segments
A line segment is the part of a line that connects two points.
It is shorter than a full line because it stops at two endpoints.
In this exercise, we draw line segments like building blocks for creating shapes.
Here鈥檚 how it鈥檚 done:
- AB: Connects A (-3, 1) to B (3, 1). This forms a horizontal segment because it does not go up or down; it stays at the same y-coordinate of 1.
- BC: Connects B (3, 1) to C (-2, -3). Here, you draw a line from a higher y-coordinate to a lower one, forming an angled line.
- CD: Connects C (-2, -3) to D (0, 3). This line moves upwards as it links a point with a lower y-coordinate to a higher one.
- DE: Connects D (0, 3) to E (2, -3). Again, you move from a higher y-coordinate to a lower one, forming a downward slope.
- EA: Connects E (2, -3) back to A (-3, 1). This segment completes our shape with an upward slope.
Slopes of Lines
The slope of a line measures how steep a line is and the direction it moves.
It's calculated by dividing the change in y-coordinates (rise) by the change in x-coordinates (run).
Slopes help to understand whether a line is rising or falling as you move across it.
- Horizontal Lines: Like AB, have a slope of zero because there is no change in y-coordinates. So, no rise but there is a lot of run.
- Negative Slopes: Represented by lines BC and DE. For these lines, the slope is negative because they run downwards from left to right. This happens when the y-value decreases as we move along the x-axis.
- Positive Slopes: Like CD and EA, these lines slope upwards. Here, the increase in y-values signifies a positive increase when moving across the x-axis.
Coordinate Plane
The coordinate plane is essentially a grid used in mathematics to plot points, lines, and shapes.
It's formed by two perpendicular lines called axes.
- X-axis: The horizontal line and it determines the x-coordinate of a point.
- Y-axis: The vertical line and it determines the y-coordinate of a point.
