EXAMPLE 10 Show that the points (a, a),(-a, - a) and (-3a, 3a) are the vertices of an equilateral triangle. Also find its area.

The triangle is not equilateral.

Step-by-step explanation:

Distance formula:

Distance from (a, a) to (-a, -a):

Distance from (-a, -a) to (-3a, 3a):

Distance from (-3a, 3a) to (a, a):

The three sides do not have the same length, so the triangle is not equilateral.

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: