Question

Point W is located on so that = . What are the coordinates of Point W?(3, 3)(6, 6)(9, 9)(2, 2)

Answer 1

Given that

`(QW)/(QR)=(3)/(4)`

The points are

`Q(3,3)\text{ and }R(11,11)`

Let the distance between Q and W is 3x and the distance between Q and R is 4x.

Consider the points

`(x_1,y_1)=(3,3)\text{ and }(x_2,y_2)=(11,11)`

Recall the formula for the distance

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`
`\text{Substitute }d=4x,x_1=3,y_1=3,x_2=11,y_2=11,\text{ we get}`

`4x=\sqrt[]{(11-3_{})^2+(11_{}-3)^2}`

`4x=\sqrt[]{8^2+8^2}=\sqrt[]{2*8^2}=8\sqrt[]{2}`
`x=(8)/(4)\sqrt[]{2}=2\sqrt[]{2}=2.828=3`

The distance between QR is

`4*3=12`

The distance between QW is

`3*3=9`

Again using the distance formula, we get

Let (x,x)=W and Q(3,3) , distance is 9.

`9=\sqrt[]{(x-3)^2+(x-3)^2}`

`81=\mleft(x-3\mright)^2+\mleft(x-3\mright)^2`

`81=2\mleft(x-3\mright)^2`
`9=\sqrt[]{2}(x-3)`
`x=9`

Hence the required point is (9,9).