n a rectangle ABCD, the slope of line AB is 1 and the slope of line BC is - 1/2. What is the slope of
(a) line AD
(b) line CD
(c) the altitude of line AD
(d) the altitude of line CD
Thanks.
This rectangle could not be a rectangle. Check the problem statement. Perhaps it is a parallelogram.
To find the slopes of lines and altitudes in a rectangle, we can use the properties of perpendicular lines and parallel lines. Let's go through each question step by step:
(a) To find the slope of line AD, we know that line AD is perpendicular to line AB (since opposite sides of a rectangle are parallel). Perpendicular lines have slopes that are negative reciprocals of each other. So if the slope of line AB is 1, the slope of line AD will be -1/1, which is -1.
(b) Similarly, line CD is perpendicular to line BC. Since the slope of line BC is -1/2, the slope of line CD will be the negative reciprocal of -1/2, which is 2.
(c) The altitude of line AD is a vertical line that is perpendicular to line AD. A vertical line has an undefined slope since its equation is x = constant. So the slope of the altitude of line AD is undefined.
(d) The altitude of line CD is also a vertical line since it is perpendicular to line CD. Hence, its slope is also undefined.
In summary:
(a) The slope of line AD is -1.
(b) The slope of line CD is 2.
(c) The slope of the altitude of line AD is undefined.
(d) The slope of the altitude of line CD is undefined.
I hope this helps! Let me know if you have any further questions.