Con Triangle ABC with vertices A(0,0),
B(0,4), and C(3,0) is dilated to
form triangle ADE. What is the
E if D has coordinates
(0,6)?
106

The coordinates of E are .

Step-by-step explanation:

The triangle ABC represents a right triangle as both sides AB and AC are orthogonal to each other. The side AB is in the y axis, whereas the side AC is in the x axis. The triangle is dilated with respect to the origin, in which point A is set.

Vectorially speaking, dilation is defined by the following operation:

(1)

Where:

- Point of reference.

- Original point.

- Dilated point.

- Dilation factor.

By applying this operation, point B becomes point D:

,

Lastly, we transform point C into point E by applying the same operation: , and

The coordinates of E are .

answer is x<

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2