Question

Consider RS endpoints R(-2,1) and S(4,4) Find point Q that is 2/3 away NEED THIS ASAP PLEASE ANSWER

Answer 1

The question does not clearly specify from which endpoint Q is at 2/3. I'll assume Q is 2/3 away from R.

Answer:

The point Q is (2,3)

Explanation:

Take the aligned points R(-2,1), S(4,4), and Q(x,y) in such a way that Q is 2/3 away from R (assumed).

The required point Q must satisfy the relation:

d(RQ) = 2/3 d(RS)

Where d is the distance between two points.

The horizontal and vertical axes also satisfy the same relation:

x(RQ) = 2/3 x(RS)

`x_R-x_Q=2/3(x_R-x_S)`

And, similarly:

`y_R-y_Q=2/3(y_R-y_S)`

Working on the first condition:

`-2-x=2/3(-2-4)=2/3(-6)`

Removing the parentheses:

`-2-x=-4`

Adding 2:

`-x = -2`

x = 2

Similarly, working with the vertical component:

`1-y=2/3(1-4)=2/3(-3)`

Removing the parentheses:

`1-y=-2`

Subtracting 1:

`-y = -3`

y = 3

The point Q is (2,3)