This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Find the midpoint of the segment AA'. The coordinates of point A are (3,3) and its image A' are (3,-3). The midpoint M of the segment AA' is given by the formula: M = ((x_1+x_2)/(2), (y_1+y_2)/(2)) Substitute the coordinates of A and A': M = ((3+3)/(2), (3+(-3))/(2)) M = ((6)/(2), (0)/(2)) M = (3,0) Step 2: Find the slope of the segment AA'. The slope m_AA' of the segment connecting A(3,3) and A'(3,-3) is given by the formula: m_AA' = (y_2-y_1)/(x_2-x_1) m_AA' = (-3-3)/(3-3) m_AA' = (-6)/(0) The slope is undefined, which means the segment AA' is a vertical line. Step 3: Determine the slope of the mirror line. The mirror line is the perpendicular bisector of the segment AA'. Since AA' is a vertical line, the mirror line must be a horizontal line. The slope of a horizontal line is 0. Step 4: Find the equation of the mirror line. The mirror line passes through the midpoint M(3,0) and has a slope of 0. Using the point-slope form of a linear equation, y - y_1 = m(x - x_1): y - 0 = 0(x - 3) y = 0 Step 5: Express the equation in the form ax+by+c=0. The equation y=0 can be written as: 0x + 1y + 0 = 0 So, the equation of the mirror line is 0x+y+0=0. That's 2 down. 3 left today — send the next one.