Math Problem Statement

In the coordinate plane, plot AB and CD given by the points A(10, -4), B(3, -4), C(-1, 2), D(-1, 5).

Solution

In this image, you are asked to plot two line segments, ABAB and CDCD, on a coordinate plane using the given points:

  • Point A(10,4)A(10, -4)
  • Point B(3,4)B(3, -4)
  • Point C(1,2)C(-1, 2)
  • Point D(1,5)D(-1, 5)

Here’s how you can plot the segments:

  1. Plot points A and B:

    • A(10,4)A(10, -4): Move to x=10x = 10 and y=4y = -4 on the coordinate plane.
    • B(3,4)B(3, -4): Move to x=3x = 3 and y=4y = -4.
    • Draw a horizontal line segment connecting these two points. Since both points share the same yy-coordinate, the line will be horizontal.
  2. Plot points C and D:

    • C(1,2)C(-1, 2): Move to x=1x = -1 and y=2y = 2.
    • D(1,5)D(-1, 5): Move to x=1x = -1 and y=5y = 5.
    • Draw a vertical line segment connecting these two points. Since both points share the same xx-coordinate, the line will be vertical.

The resulting graph should show:

  • A horizontal line segment ABAB from (10,4)(10, -4) to (3,4)(3, -4).
  • A vertical line segment CDCD from (1,2)(-1, 2) to (1,5)(-1, 5).

Would you like more details on how to compute slope or distance for these segments? Or do you have any other questions?

Here are 5 related questions:

  1. What is the distance between points AA and BB?
  2. What is the distance between points CC and DD?
  3. How do we calculate the slope of a line segment between two points?
  4. What is the midpoint of the segment ABAB?
  5. What is the equation of the line through points CC and DD?

Tip: When two points share the same xx-coordinate, the line between them is vertical; when they share the same yy-coordinate, the line is horizontal.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Line Segments
Plotting Points

Formulas

Distance between two points formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
Slope of a line: m = (y2 - y1) / (x2 - x1)

Theorems

Basic Coordinate Geometry

Suitable Grade Level

Grades 7-9