If point C(1, 2) and point D(7, 8) are given, what is the coordinates of the poi

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Question: If point C(1, 2) and point D(7, 8) are given, what is the coordinates of the point that divides CD in the ratio 3:2?

Options:

Correct Answer: (4, 5)

Solution:

Using the section formula: P = ((3*7 + 2*1)/(3+2), (3*8 + 2*2)/(3+2)) = (4, 5).

If point C(1, 2) and point D(7, 8) are given, what is the coordinates of the point that divides CD in the ratio 3:2?

If point C(1, 2) and point D(7, 8) are given, what is the coordinates of the point that divides CD in the ratio 3:2?

Step 1: Identify the coordinates of points C and D. C is (1, 2) and D is (7, 8).
Step 2: Understand that we need to divide the line segment CD in the ratio 3:2.
Step 3: Use the section formula, which is: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m and n are the parts of the ratio.
Step 4: In our case, m = 3, n = 2, x1 = 1, y1 = 2, x2 = 7, and y2 = 8.
Step 5: Calculate the x-coordinate of point P using the formula: P_x = (3*7 + 2*1)/(3+2).
Step 6: Calculate: P_x = (21 + 2)/5 = 23/5 = 4.6.
Step 7: Calculate the y-coordinate of point P using the formula: P_y = (3*8 + 2*2)/(3+2).
Step 8: Calculate: P_y = (24 + 4)/5 = 28/5 = 5.6.
Step 9: The coordinates of point P that divides CD in the ratio 3:2 are (4.6, 5.6).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment into a specific ratio.
Coordinate Geometry – Understanding how to work with coordinates and apply geometric formulas in a Cartesian plane.