In a rectangle ABCD, the slope of line AB is 1 and the slope of line BC is -1/2. What is the slope of the altitude to line AD the altitude to line CD.

Thanks in advance.

How are you defining altitude? Normally, I would measure altitude perpendicular to either the axis coordinate, OR perpendicular to a side of the rectangle.

To find the slope of the altitude to line AD and the altitude to line CD in a rectangle ABCD, we can use a property of perpendicular lines.

Step 1: Understand the problem
In a rectangle, opposite sides are parallel, so lines AB and CD are parallel. The slope of line AB is given as 1, and the slope of line BC is given as -1/2.

Step 2: Find the slope of line CD
Since line CD is parallel to line AB, it has the same slope. Therefore, the slope of line CD is also 1.

Step 3: Find the slope of the altitude to line AD
The altitude to line AD is perpendicular to line AD. So, we need to find the negative reciprocal of the slope of line AD to get the slope of the altitude.

The slope of line AD is the negative reciprocal of the slope of line AB, which is -1. Therefore, the slope of the altitude to line AD is 1.

Therefore, the slope of the altitude to line AD is 1, and the slope of the altitude to line CD is also 1.