Math Problem Statement

Given the directed line segment from A to B, construct the point P that divides the segment in a given ratio from A to B.

Solution

The problem you're asking about involves finding the point PP on a line segment from AA to BB that divides the segment in a given ratio. The ratio is provided as 1:2.

This is a typical application of the section formula, which allows you to find a point that divides a line segment in a specific ratio.

The formula for a point P(x,y)P(x, y) dividing a line segment joining A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2) in the ratio m:nm:n is given by:

P(x,y)=(mx2+nx1m+n,my2+ny1m+n)P(x, y) = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)

Given the ratio 1:2, we can apply the formula by substituting the appropriate values. Could you provide the coordinates of points AA and BB? This way, I can help you calculate the exact location of point PP.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Section Formula

Formulas

Section formula P(x, y) = ((mx2 + nx1) / (m+n), (my2 + ny1) / (m+n))

Theorems

Section formula theorem

Suitable Grade Level

Grades 9-12