The area of a quadrilateral whose vertices are (3,0), (4,5), (-1,4) and (-2,-1) taken in order, is:
24 sq. units
The area of a quadrilateral given its vertices \((x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4)\) is calculated using the formula: \[ \text{Area} = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1) \right| \] Substituting the given coordinates: \[ \text{Area} = \frac{1}{2} \left| (3 \times 5) + (4 \times 4) + (-1 \times -1) + (-2 \times 0) - (0 \times 4 + 5 \times -1 + 4 \times -2 + -1 \times 3) \right| \] \[ = \frac{1}{2} \left| (15 + 16 + 1 + 0) - (0 -5 -8 -3) \right| \] \[ = \frac{1}{2} \left| 32 - (-16) \right| = \frac{1}{2} \times 48 = 24 \] Thus, the area is **24 square units**.
Important Questions from Co-ordinate Geometry
In which quadrant is the point (–4, –3) located?
A. I
B. II
C. III
D. IV
The coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4) is:
The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
In ΔABC if ∠A = 50° and ∠B = 70°, find the measure of exterior angle A.
