Question

Line AB has a slope of 2. The point is at the origin, (0, 0).

Find coordinates for D so that line AB is parallel to line CD. Write your answer as an ordered pair: D (,)
a) D (1, 2)
b) D (2, 4)
c) D (-1, -2)
d) D (-2, -4)

Find coordinates for E so that line AB is perpendicular to line CE. Write your answer as an ordered pair: E (,)
a) E (2, -1)
b) E (-2, 1)
c) E (1, -2)
d) E (-1, 2)

Answer 1

To find a point D that is parallel to line AB, we use the same slope as line AB and the x-coordinate of the origin to get the coordinate (0, 2). To find a point E that is perpendicular to line AB, we use the negative reciprocal of the slope of line AB and the x-coordinate of the origin to get the coordinate (2, -1).

Step-by-step explanation:

To find coordinates for point D such that line AB is parallel to line CD, we need to find a point on line CD that has the same slope as line AB. Since line AB has a slope of 2, we can use this slope to find the y-coordinate of point D. Since the point is at the origin (0, 0), the x-coordinate of point D will be the same as line AB. Therefore, the coordinates for point D are (0, 0+2) = (0, 2). So, the correct answer is a) D (1, 2).

To find coordinates for point E such that line AB is perpendicular to line CE, we need to find a line with a slope that is the negative reciprocal of the slope of line AB. Since line AB has a slope of 2, the slope of line CE will be -1/2. Since the point is at the origin (0, 0), the x-coordinate of point E will be the same as line AB. Therefore, to find the y-coordinate of point E, we can use the equation y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through the origin, the y-intercept is 0. Therefore, the equation becomes y = -1/2x + 0. Plugging in x = 2, we get y = -1/2(2) + 0 = -1. So, the correct answer is a) E (2, -1).