Question

In the figure the coordinates of the endpoints of a line are given. The point P divides the line in the ratio 2:3. The coordinates of P are:

• A. (8, 6)
• B. (8, 7)
• C. (7, 7)
• D. (7, 6)

Answer 1

Answer:

D. (7, 6)

To find the coordinates of point P, we use the section formula. The formula for a point P(x, y) that divides a line segment with endpoints

$(x_1,y_1)$and $(x_2,y_2)$ in the ratio m:n is:

$P(x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

From the given information:

• Endpoint 1: $(x_1,y_1)= (3, 4)$

• Endpoint 2: $(x_2,y_2)=(13,9)$

• Ratio: m:n = 2:3

Now, we can substitute these values into the formula to find the coordinates of P.

Therefore, the coordinates of point P are (7, 6).