Question

Dionne plans to change her yard and would like at least part of the picnic table to be shaded by the umbrella at mid-day.

Determine whether each option below would result in any part of the picnic table being shaded by the umbrella at mid-
day. Explain how you know.
• Option A: Rotate the picnic table 90° clockwise about the point (5, 0).
Option B: Move the umbrella to a location 4 feet to the left and 1 foot down.
• Option C: Move the umbrella to a location 3 feet down and 2 feet to the left.
Enter your answers and explanations in the space provided

Answer 1

• Option C

Explanation:

Refer to attached picture

At midday the shaded area is going to be under the umbrella only, therefore the option moving the table under the umbrella will be the answer.

So the options:

Option A: Rotate the picnic table 90° clockwise about the point (5, 0)

• No. The table has dimensions of 4x3, after this rotation the distance between the umbrella and the table will be zero but the table won't go under the umbrella.

Option B: Move the umbrella to a location 4 feet to the left and 1 foot down.

• No. The movement will bring the umbrella down by one feet and no intersections.

Option C: Move the umbrella to a location 3 feet down and 2 feet to the left.

• Yes. By moving the umbrella down by 3 feet and to the left by 2 feet, it will cover some part of the table. The lowest point of the umbrella will have the coordinate of (5, 1). So this is the correct option