3.Point P lies on the directed line segment from A (2,3) to B(8,0) and partitions the segment in the ratio 2 to 1. What is the x-coordinate of point P?

4. Determine the area of the rectangle ABCD with vertices A(−1,−1), B(2,3), C(10,−3), D(7,−7)

3. The x-coordinate of point P is 6. Since P(6,1).

4. Area of rectangle is 32 square units.

Step-by-step explanation:

3. The directed segment AB on the Cartesian plane shows that it has a length of 6 units. Since point P partitions the segment in a given ratio 2:1, then its coordinate would be the one that divides segment AB into 4:2. This coordinate is (6, 1). Thus, the x-coordinate of point P is 6.

4. The appropriate sketch of the rectangle in a Cartesian plane shows that;

AB = DC = 4 units

AD = BC = 8 units

Area of rectangle = length x width

                             = 8 x 4

                             = 32 square units

The area of the rectangle is 32 square units.