Question

In the diagram, AB is divided into equal parts. The coordinates of point A are _____, and the coordinates of point I are______ .

Answer 1

The coordinates of point A are (-10,-4). The coordinates of I are (-3.875,-10.125).

Explanation:

It is given that the the line AB is divided into equal parts. Therefor distance between two consecutive points are equal.

The point D is mid point of A and F.

`(x,y)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

`(-8.25,-5.75)=((x+(-6.5))/(2),(y+(-7.5))/(2))`

`-8.25=(x-6.5)/(2)`

`-16.50=x-6.5`

`-10=x`

`-5.75=(y-7.5)/(2)`

`-11.50=y-7.5`

`-4=y`

Therefore the coordinates of A are (-10,-4).

Similarly the pint H is midpoint of F and B.

`(-4.75,-9.25)=((x+(-6.5))/(2),(y+(-7.5))/(2))`

The values of x and y are,

`x=-3`

`y=-11`

Therefore the coordinates of B are (-3,-11).

The point I is mid point of HB. H(-4.75,-9.25) and B(-3,-11).

`(x,y)=((-4.75-3)/(2),(-9.25-11)/(2))`

`(x,y)=(-3.875,-10.125)`

Therefore the coordinates of I are (-3.875,-10.125).