What is the coordinates of the point that divides the line segment joining (6, 8

₹0.0

Question: What is the coordinates of the point that divides the line segment joining (6, 8) and (2, 4) in the ratio 1:1?

Options:

Correct Answer: (4, 6)

Solution:

Using the section formula: P = ((1*2 + 1*6)/(1+1), (1*4 + 1*8)/(1+1)) = (4, 6).

What is the coordinates of the point that divides the line segment joining (6, 8) and (2, 4) in the ratio 1:1?

What is the coordinates of the point that divides the line segment joining (6, 8) and (2, 4) in the ratio 1:1?

Step 1: Identify the two points given in the question. They are (6, 8) and (2, 4).
Step 2: Understand that we need to find a point that divides the line segment between these two points in the ratio 1:1.
Step 3: Recall the section formula, which is used to find a point that divides a line segment. The formula is: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m and n are the ratios.
Step 4: In our case, m = 1 and n = 1 because the ratio is 1:1.
Step 5: Substitute the coordinates of the points into the formula. Here, (x1, y1) = (6, 8) and (x2, y2) = (2, 4).
Step 6: Calculate the x-coordinate: P_x = ((1*2 + 1*6)/(1+1)) = (2 + 6)/2 = 8/2 = 4.
Step 7: Calculate the y-coordinate: P_y = ((1*4 + 1*8)/(1+1)) = (4 + 8)/2 = 12/2 = 6.
Step 8: Combine the x and y coordinates to get the final point: P = (4, 6).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment into a specific ratio.