Question

A, B, C, and D are four points on a plane such that AB = CD = 2 units and AB ∦ CD. How many different locations of P can you find such that the areas of Triangle ABP and Triangle CDP are 2 and 3 square units, respectively?

a) 0
b) 1
c) 2
d) 3

Answer 1

To find the location of P such that the areas of Triangle ABP and Triangle CDP have specific values, we consider the properties of triangles and their areas. The answer is 1.

Step-by-step explanation:

To find the locations of point P such that the areas of Triangle ABP and Triangle CDP have specific values, we need to consider the properties of triangles and their areas.

1. Let's start with Triangle ABP, which has an area of 2 square units. Since the base AB has length 2 units, the height of Triangle ABP must be 1 unit.
2. Next, consider Triangle CDP, which has an area of 3 square units. Since the base CD has length 2 units, the height of Triangle CDP must be 1.5 units.
3. Since the triangles have different heights, there can only be one location for point P that satisfies both conditions. Therefore, the answer is (b) 1.