University:
Jackson College
Course:
MAT-039 | Beginning Algebra
Academic year:

2024
Views:

342

Pages:

48
Author:

metalkadf9w

Characteristics of Linear Relations Lesson #1: Line Segments on a Cartesian Plane Unit Overview The graph of a linear relation is represented by a straight line. The line can be infinite or finite depending on the domain and range of the linear relation. In some cases, we are only interested in a portion of a line. This portion is called a line segment. We have already studied some of the characteristics of the graph of a linear relation: intercepts, domain, and range. In this unit, we study some characteristics of line segments: namely, length, midpoint, distance, and slope. We demonstrate an understanding of slope with respect to rise and run, the slope formula, and rate of change. We then discuss the slopes of parallel and perpendicular lines. Line Segment A line segment is the portion of a line between two points on the line. If the endpoints of a line segment are A and B, we refer to it as line segment AB. NOTE: Line segment AB may also be written as AB. Length of a Horizontal Line Segment Consider the line segments shown on the grid. a) Find the length of each line segment by counting. length of AB is 10 units. length of CD is 4 units. length of EF is 7 units. b) Determine the coordinates of the endpoints of each line segment. AB → A(2, 8), B(8, 8) CD → C(3, 4), D(7, 4) EF → E(-9, -6), F(-2, -6) c) Complete the following. The difference in the x-coordinates, (x_B - x_A), is 6. The difference in the x-coordinates, (x_D - x_C), is 4. The difference in the x-coordinates, (x_F - x_E), is 7. d) How can the coordinates of the endpoints of a horizontal line segment be used to find the length of the line segment? Subtract the x-coordinate of the left endpoint from the x-coordinate of the right endpoint. length = right - left Characteristics of Linear Relations Lesson #1: Line Segments on a Cartesian Plane Class Ex. #1 a) Line segment AB has endpoints A(2, 8) to B(-5, 8). Determine the length of AB. length = xB - xA = (-5) - 2 = -7 b) Determine the length of the line segment from P(a-2, b) to Q(a+4, b). length = xQ - xP = (a + 4) - (a - 2) = 6 Length of a Vertical Line Segment Consider the line segments shown on the grid. a) Find the lengths of each line segment by counting. length of GH is 12 units. length of IJ is 5 units. length of KL is 5 units. b) Determine the coordinates of the endpoints of each line segment. GH → G(-5, -8), H(-3, 4) IJ → I(1, 2), J(1, 7) KL → K(6, -8), L(6, -2) c) Complete the following: The difference in the y-coordinates, yJ - yI, is 5. The difference in the y-coordinates, yL - yK, is 6. d) How can the coordinates of the endpoints of a vertical line segment be used to find the length of the line segment? Subtract the y-coordinate of the lower endpoint from the y-coordinate of the higher endpoint. length = higher - lower Class Ex. #2 a) Line segment RS has endpoints R(1, -4) to S(1, -9). Determine the length of RS. length = yS - yR = (-9) - (-4) = -5 b) Determine the length of the line segment from P(a, b) to Q(a, b+10). length = yQ - yP = (b + 10) - b = 10