InfyTQ Geometry Quiz 2

C. The area of a circle is given by the formula A = ², where r is the radius of the circle. The problem provides the diameter of the circle, which is twice the radius. So,

Now substitute this value into the area formula and calculate the area.

​

​

2^nd and 4^th quadrant have different signs

Applying the formula,

(y₂-y₁)/(x₂ -x₁)
= \frac{7-3}{2-(-2)}
= \frac{4}{4}
= 1

solution:

The slope of the line = 2
C= -3
Substituting values in the equation, we get
Y = mx + c
We get
Y = 2x – 3

The line segment joining the points A(2,4) and B(7,9).

Let point P divides the line segment AB internally in the ratio 2:3.

The section formula is

P = \left ( \frac{x_{2}m +x_{1}n}{m + n}, \frac{y_{2}m + y_{1}n}{m+n} \right )

P = \left ( \frac {7(2)+ 2(3)}{2 + 3}, \frac{9(2) + 4(3)}{2+3} \right )

P = \left ( \frac {14+6}{5}, \frac{18 + 12}{5} \right )

P = \left ( \frac {20}{5}, \frac{30}{5} \right )

P = (4,6)

 

Formula for calculating area of triangle when vertices are given,
= 1/2[x₁( y₂ - y₃ )+ x₂ (y₃ –y₁)+ x₃(y₁ –y₂)]
= 1/2 [4 (12 + 2) + 10 (-2-5) + (-3) (5 - 12)]
= 0.5 square units

The distance between the points (1,3) and (2,4) is

Point 1(x_A,y_A) = (1, 3)

Point 2(x_B,y_B) = (2, 4)

Formula :

Distance between two points = √(x_B−x_A)² + (y_B−y_A)²

Solution :

Distance between two points = √(2−1)² + (4−3)²

= √1²+1²

= √1+1

= √2 = 1.414

Area = 1/2 [0 (0 - 0) + 2 (0 -0) + 3 (0 - 0)]
= 0
Since all the three points are collinear, the area will be 0.

Using a formula to calculate the centroid of the triangle
= \farc{9+2+1}{3}, {0+8+4}{3}
= (4, 4)

Distance = √(5²+0²)
= 5