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)
Question
Answer:
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.