Find the coordinates of the point that divides the line segment joining (3, 4) a

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Question: Find the coordinates of the point that divides the line segment joining (3, 4) and (9, 10) in the ratio 1:1.

Options:

Correct Answer: (6, 7)

Solution:

Using the section formula: P = ((1*9 + 1*3)/(1+1), (1*10 + 1*4)/(1+1)) = (6, 7).

Find the coordinates of the point that divides the line segment joining (3, 4) and (9, 10) in the ratio 1:1.

Find the coordinates of the point that divides the line segment joining (3, 4) and (9, 10) in the ratio 1:1.

Step 1: Identify the two points given in the problem. They are (3, 4) and (9, 10).
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 in a given ratio. The formula is: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m and n are the parts of the ratio, and (x1, y1) and (x2, y2) are the coordinates of the two points.
Step 4: In our case, the ratio is 1:1, so m = 1 and n = 1.
Step 5: Substitute the coordinates of the points into the formula. Here, (x1, y1) = (3, 4) and (x2, y2) = (9, 10).
Step 6: Calculate the x-coordinate: P_x = (1*9 + 1*3) / (1 + 1) = (9 + 3) / 2 = 12 / 2 = 6.
Step 7: Calculate the y-coordinate: P_y = (1*10 + 1*4) / (1 + 1) = (10 + 4) / 2 = 14 / 2 = 7.
Step 8: Combine the x and y coordinates to get the final point: P = (6, 7).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
Ratio Division – Understanding how to apply the ratio to the coordinates of the endpoints to find the dividing point.