Question

Determine the point that is 3/4 the distance from the endpoint (−6,−16)(−6,−16) of the segment with endpoints (34,2)(34,2) and (−6,−16)(−6,−16).

what, pls explain cus there is other questions similar to this​

Answer 1

The location of the point that is 3/4 the distance from
`A(x,y)` is
`C(x,y) = (24, -2.5)`.

Explanation:

Let
`A(x,y) = (-6,-16)` and
`B(x,y) = (34,2)` the endpoints of the segment, we can determine the location of the point that is 3/4 the distance from
`A(x,y)` by the following vector equation:

`C(x,y) = A(x,y) + (3)/(4)\cdot (B(x,y)-A(x,y))` (1)

If we know that
`A(x,y) = (-6,-16)` and
`B(x,y) = (34,2)`, the location of
`C(x,y)` is:

`C(x,y) = (-6,-16)+(3)/(4)\cdot [(34,2)-(-6,-16)]`

`C(x,y) = (-6,-16)+(3)/(4)\cdot (40,18)`

`C(x,y) = (24, -2.5)`

The location of the point that is 3/4 the distance from
`A(x,y)` is
`C(x,y) = (24, -2.5)`.