Find the midpoint of a line joining the points A(2, 2) and B(6, 4).

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6. Find the midpoint of a line joining the points A(2, 2) and B(6, 4).

Recall the midpoint formula.
The midpoint $(x_m, y_m)$ of a line segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$x_m = \frac{x_1 + x_2}{2}$ $y_m = \frac{y_1 + y_2}{2}$
Substitute the given coordinates into the formula.
Given points A(2, 2) and B(6, 4), we have $x_1 = 2$ , $y_1 = 2$ , $x_2 = 6$ , and $y_2 = 4$ .
$x_m = \frac{2 + 6}{2}$ $y_m = \frac{2 + 4}{2}$
Calculate the coordinates of the midpoint.
$x_m = \frac{8}{2} = 4$ $y_m = \frac{6}{2} = 3$
The midpoint is $(4, 3)$ .

The final answer is $\boxed{\text{C. } (4, 3)}$ .

7. A bag contains 3 green and 2 brown identical balls. If 2 balls are picked at random from the bag one after the other without replacement, find the probability that they are of the same colour.
Determine the total number of balls in the bag.
Number of green balls = 3
Number of brown balls = 2
Total number of balls = $3 + 2 = 5$ .
Calculate the probability of picking two green balls (GG).
The probability of picking the first green ball is $\frac{3}{5}$ .
After picking one green ball, there are 2 green balls left and a total of 4 balls.
The probability of picking a second green ball (given the first was green) is $\frac{2}{4}$ .
$P(\text{GG}) = \frac{3}{5} \times \frac{2}{4} = \frac{6}{20} = \frac{3}{10}$
Calculate the probability of picking two brown balls (BB).
The probability of picking the first brown ball is $\frac{2}{5}$ .
After picking one brown ball, there is 1 brown ball left and a total of 4 balls.
The probability of picking a second brown ball (given the first was brown) is $\frac{1}{4}$ .
$P(\text{BB}) = \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10}$
Calculate the probability that both balls are of the same color.
This is the sum of the probabilities of picking two green balls or two brown balls.
$P(\text{Same Color}) = P(\text{GG}) + P(\text{BB})$ $P(\text{Same Color}) = \frac{3}{10} + \frac{1}{10}$ $P(\text{Same Color}) = \frac{4}{10}$ $P(\text{Same Color}) = \frac{2}{5}$
The final answer is $\boxed{\frac{2}{5}}$ .

Find the midpoint of a line joining the points A(2, 2) and B(6, 4).

Step-by-step solution

Recall the midpoint formula.

Substitute the given coordinates into the formula.

Calculate the coordinates of the midpoint.

Determine the total number of balls in the bag.

Calculate the probability of picking two green balls (GG).

Calculate the probability of picking two brown balls (BB).

Calculate the probability that both balls are of the same color.

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