See the attached figure. The original triangle is shown in red (triangle ABC). The line of reflection is the blue dashed line. This is the equation y = x. Reflecting triangle ABC over the line y = x results in the purple triangle A'B'C'.
Note how the x and y values swap places.
We have...
point A = (5,1) turn into point A' = (1,5)
point B = (8,1) turn into point B' = (1,8)
point C = (8,6) turn into point B' = (6,8)
The swap occurs because the rule (x,y) --> (y,x) tells this to happen.
The purple triangle is the final answer.
The answer would be letter B. You can see that the price of the demanded products as the time passes by decreases. So the answer is letter B.
Simplifying
j = (2j + 3)
Reorder the terms:
j = (3 + 2j)
Remove parenthesis around (3 + 2j)
j = 3 + 2j
Solving
j = 3 + 2j
Solving for variable 'j'.
Move all terms containing j to the left, all other terms to the right.
Add '-2j' to each side of the equation.
j + -2j = 3 + 2j + -2j
Combine like terms: j + -2j = -1j
-1j = 3 + 2j + -2j
Combine like terms: 2j + -2j = 0
-1j = 3 + 0
-1j = 3
Divide each side by '-1'.
j = -3
Simplifying
j = -3
Step-by-step explanation:
The vertex is the point (-4, 7).
Multiply numerator and denominator by the conjugate of the denominator
Denominator: -10 + 8i
Conjugate of the denominator: -10 - 8i
Operation:
[9 +7i] / [-10 + 8i] * [-10 -8i] / [-10 - 8i] = [-90 - 72i - 70i +56] / [100 + 64] =
[-34 -142i] / 164 = [-17 -71i] / 82