Question

The vector v=(7,1) lies entirely in quadrant 1. Give possible coordinates for the initial point and terminal point of the vector. Show your work and explain your reasoning

Answer 1

A possible initial point is (1,4) and a possible terminal point is (8,5)

Explanation:

The given vector is
`\vec{v}=(7,1)`.

We can rewrite this vector as:

`\vec{v}=\binom{7}{1}`

The x-components is 7 and the y-component is 1.

We can choose initial point (a,b) and terminal point (c,d) in the first quadrant such that
`c-a=7` and
`d-b=1`

If a=1, and b= 4, then:

`c-1=7` and
`d-4=1`

This implies that:

`c=7+1=8` and
`d=1+4=5`

Therefore a possible initial point is (1,4) and a possible terminal point is (8,5)