Question

Given H(6, 7) and I(-7,-6), if point G lies 1/2 of the way along Hl. John says that point G is located at the origin. Is John correct? Justify your answer.

Answer 1

Given:

Two points are (6, 7) and I(-7,-6).

Point G lies
`(1)/(2)` of the way along Hl.

John says that point G is located at the origin.

To find:

Whether John is correct or not.

Solution:

Point G lies
`(1)/(2)` of the way along Hl. I means point G is the midpoint of HI.

`Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

`G=\left((6-7)/(2),(7-6)/(2)\right)`

`G=\left((-1)/(2),(1)/(2)\right)`

The location of point G is at
`\left((-1)/(2),(1)/(2)\right)`, which is not equal to origin, i.e., (0,0).

Therefore, John is incorrect.