Can anyone give a hint here?

In square ABCD, point M is the midpoint of CD. Find the ratios of the areas of the four reigons that are formed.

blackpanther Dec 31, 2023

#1**+1 **

For convenience, let the sides of the square = 2

Let

B = (0,0)

C= (2,0)

D =(2,2)

A =(0,2)

M = (2,1)

Line through AC has the slope -1

The equation of this line is y= -1 (x -2) = -x + 2

Line through BM has a sloe of (1/2)

Equation of this line is y = (1/2)x

x intersection of these two lines

-x + 2 = (1/2)x

2 = (3/2)x

x = 4/3

y = (1/2)(4/3) = (4/6) = (2/3)

So the coordinates of P =( 4/3 , 2/3)

Area of BPC = (1/2)(BC)(2/30 = (1/2)(2)(2/3) = 2/3

Area of APB = (1/2) (AB)(4/3) = (1/2)(2)(4/3) = 4/3

Area of MPC = (1/2)(MC) (2 -4/3) =( 1/2) (1) (2 - 4/3) = (1/2)(2/3) = 2/6 = 1/3

Area of APMD = area of square less the other areas = 4 - 2/3 - 4/3 - 1/3 = 4 - 7/3 = 12/3 - 7/3 = 5/3

The problem wants to find the ratios of the areas to each other ???....if so

MPC : BPC : APB : APMD = 1 : 2 : 4 : 5

CPhill Jan 1, 2024