Question

Find the point y on ab such that the ratio of ay to yb is 1:2?

Answer 1

y = (-1,1)

Explanation:

If a point y
`(x_p,y_p)` divides a line A
`(x_1,y_1)` B
`(x_2,y_2)` in the ratio a:b, the formula to find the coordinates of the point y is:

`x_p=x_1+(a)/(a+b)(x_2-x_1)`

and

`y_p=y_1+(a)/(a+b)(y_2-y_1)`

We know Point A is (-3,4) and Point B is (3,-5). And the ratio is a:b or 1:2, so we can say:

`x_1` = -3

`x_2` = 3

`y_1` = 4

`y_2` = -5

a = 1

b = 2

Plugging these into the formula, we get:

`x_p=-3+(1)/(1+2)(3--3)\\x_p=-3+(1)/(3)(6)\\x_p=-1`

and

`y_p=4+(1)/(1+2)(-5-4)\\y_p=4+(1)/(3)(-9)\\y_p=1`

So the point y is (-1,1)