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

here are the solutions to the next two problems. 6. Find the midpoint of a line joining the points A(2, 2) and B(6, 4). Step 1: 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 = (x_1 + x_2)/(2) y_m = (y_1 + y_2)/(2) Step 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 = (2 + 6)/(2) y_m = (2 + 4)/(2) Step 3: Calculate the coordinates of the midpoint. x_m = (8)/(2) = 4 y_m = (6)/(2) = 3 The midpoint is (4, 3). The final answer is 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. Step 1: 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. Step 2: Calculate the probability of picking two green balls (GG). The probability of picking the first green ball is (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 (2)/(4). P(GG) = (3)/(5) × (2)/(4) = (6)/(20) = (3)/(10) Step 3: Calculate the probability of picking two brown balls (BB). The probability of picking the first brown ball is (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 (1)/(4). P(BB) = (2)/(5) × (1)/(4) = (2)/(20) = (1)/(10) Step 4: 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(Same Color) = P(GG) + P(BB) P(Same Color) = (3)/(10) + (1)/(10) P(Same Color) = (4)/(10) P(Same Color) = (2)/(5) The final answer is (2)/(5). What's next?