Answer:
coordinate of point A is (a,b)
coordinate of point C is (2c,d)
slope of AD and BC =![\frac{b}{a-c}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba-c%7D)
Step-by-step explanation:
According to midpoint formula
If we have points P
and Q
then the coordinate (x,y) of mid point of line PQ is given by
and ![y=\frac{y_{1} +y_{2} }{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7By_%7B1%7D%20%2By_%7B2%7D%20%7D%7B2%7D)
now from the given diagram A is the mid point of line joining R(0,0) and S(2a,2b)
Using midpoint formula, coordinates of point A is given by
and ![y=\frac{0+2b}{2} =b](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B0%2B2b%7D%7B2%7D%20%3Db)
so we have
coordinate of point A is (a,b)
Also C is the midpoint of line joining T (2c,2d) and V(2c,0)
coordinate of point C is given by
and ![y=\frac{2d+0}{2} =d](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2d%2B0%7D%7B2%7D%20%3Dd)
so we have
coordinate of point C is (2c,d)
it is given that coordinate of point B is (a+c, b+d) and coordinate of D is (c,0)
If we have points P
and Q
then the slope of PQ =![\frac{y_{2} -y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D%20-y_%7B1%7D%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
hence slope of AD= ![\frac{0-b }{c-a}](https://tex.z-dn.net/?f=%5Cfrac%7B0-b%20%7D%7Bc-a%7D%20)
=![\frac{-b}{c-a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7Bc-a%7D)
=![\frac{-b}{-(a-c)}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B-%28a-c%29%7D)
=![\frac{b}{a-c}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba-c%7D)
and slope of BC =![\frac{d-(b+d)}{2c-(a+c)}](https://tex.z-dn.net/?f=%5Cfrac%7Bd-%28b%2Bd%29%7D%7B2c-%28a%2Bc%29%7D)
=![\frac{d-b-d}{2c-a-c}](https://tex.z-dn.net/?f=%5Cfrac%7Bd-b-d%7D%7B2c-a-c%7D)
=![\frac{-b}{c-a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7Bc-a%7D)
=![\frac{b}{a-c}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba-c%7D)
so we have
slope of AD and BC =![\frac{b}{a-c}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba-c%7D)