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

$\frac{QW}{QR}=\frac{3}{4}$

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\times8^2}=8\sqrt[]{2}$$x=\frac{8}{4}\sqrt[]{2}=2\sqrt[]{2}=2.828=3$

The distance between QR is

$4\times3=12$

The distance between QW is

$3\times3=9$

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).