Question

write an equation for the line of reflection in each item below. (do not use spaces!)
line of reflection (do not use spaces!):

Explanation:

Step1: Identify symmetry axis

The two triangles are symmetric about the y - axis? Wait, no, looking at the x - coordinates. The left triangle has a vertex at x=-2? Wait, no, let's check the vertical line. The left figure is on the left of x = -1? Wait, no, let's see the middle line. Wait, the two figures are symmetric about the line x=-1? No, wait, looking at the grid, the left triangle's right side is at x=-2? Wait, no, the vertical line of symmetry: for a reflection, the line of reflection is the perpendicular bisector between corresponding points. Let's take a point from each triangle. For example, the top vertex of the left triangle: let's say its x - coordinate is -2, and the top vertex of the right triangle is at x = 0? No, wait, the left triangle's right edge is at x=-2? Wait, no, the grid: the x - axis has marks at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. Wait, the left triangle: let's see the base. The left triangle's base is from x=-6 to x=-2? No, the right triangle's base is from x=2 to x=-2? Wait, no, the two triangles: the left one is on the left of x=-1? Wait, no, the line of reflection is the vertical line that is the mirror. Wait, actually, looking at the figure, the left triangle and the right triangle are symmetric about the line x=-1? No, wait, let's check the x - coordinates of corresponding points. Let's take a point from the left triangle: say the bottom right corner of the left triangle is at (-4, -3)? No, the bottom right corner of the left triangle: looking at the grid, the left triangle's bottom right is at x=-2, y=-3? And the bottom left corner of the right triangle is at x=0, y=-3? No, that can't be. Wait, maybe the line of reflection is x=-1? No, wait, the correct line: the two triangles are symmetric about the vertical line x=-1? No, wait, let's count the units. The left triangle is 2 units to the left of x=-1, and the right triangle is 2 units to the right? No, wait, the left triangle's right side is at x=-2, and the right triangle's left side is at x=0? No, that's 2 units apart. The midpoint between x=-2 and x=0 is x=(-2 + 0)/2=-1. Wait, no, (-2 + 0)/2=-1? No, (-2 + 0)/2=-1? Wait, -2 and 0: midpoint is -1. But looking at the figure, the left triangle is from x=-6 to x=-2? No, the right triangle is from x=2 to x=-2? Wait, no, the base of the left triangle: from x=-6 to x=-2, and the base of the right triangle: from x=-2 to x=2? Wait, no, the two triangles share the base at x=-2? No, the figure shows two triangles, one on the left of x=-1 and one on the right? Wait, no, the correct line of reflection is x=-1? No, wait, actually, looking at the grid, the left triangle is symmetric to the right triangle about the line x=-1? No, wait, the line of reflection is x=-1? Wait, no, let's look again. The left triangle: its right edge is at x=-2, and the right triangle's left edge is at x=0. The midpoint between x=-2 and x=0 is x=(-2 + 0)/2=-1. But wait, the vertical line x=-1? No, wait, the figure: the left triangle is on the left of x=-1, and the right triangle is on the right? No, the correct line is x=-1? Wait, no, maybe I made a mistake. Wait, the two triangles: the left one has a vertex at x=-2 (top), and the right one has a vertex at x=0 (top)? No, the top vertex of the left triangle is at x=-2, y=8, and the top vertex of the right triangle is at x=0, y=8? No, looking at the grid, the top vertex of the left triangle is at x=-2, y=8, and the top vertex of the right triangle is at x=0, y=8? No, that can't be. Wait, the grid lines: the x - axis, each grid square is 1 unit. So the left triangle: top at (-2,8), and the right triangle: top at (0,8)? No, the distance between -2 and 0 is 2 units, so the midpoint is at x=-1. But the line of reflection should be the vertical line that is the mirror. Wait, actually, the correct line of reflection is x=-1? No, wait, maybe I messed up. Wait, the two triangles: the left one is from x=-6 to x=-2, and the right one is from x=2 to x=-2? No, the base of both triangles is from x=-2 to x=2? No, the left triangle's base is from x=-6 to x=-2, and the right triangle's base is from x=2 to x=-2? No, that's not. Wait, the figure shows two triangles, one on the left of x=-1 and one on the right, symmetric about x=-1? No, wait, the correct line is x=-1? Wait, no, let's check the vertices. The top vertex of the left triangle: let's say it's at (-3,8), and the top vertex of the right triangle is at (1,8)? No, that's not. Wait, the correct way: the line of reflection is the vertical line that is the axis of symmetry. Looking at the figure, the two triangles are symmetric about the line x=-1? No, wait, the left triangle is to the left of x=-1, and the right triangle is to the right of x=-1, with equal distance from x=-1. Wait, no, actually, the line of reflection is x=-1? No, wait, the correct answer is x=-1? No, wait, let's look at the x - coordinates. The left triangle's right side is at x=-2, and the right triangle's left side is at x=0. The midpoint between -2 and 0 is x=-1. So the line of reflection is x=-1? Wait, no, maybe the line is x=-1? Wait, no, the figure: the left triangle and the right triangle are symmetric about the vertical line x=-1. Wait, no, maybe I made a mistake. Wait, the correct line of reflection is x=-1? No, wait, the grid: the x - axis, each square is 1 unit. The left triangle: let's take a point ( - 4, - 3) and the right triangle has a point (0, - 3). The midpoint between - 4 and 0 is - 2? No, (-4 + 0)/2=-2. Wait, that's different. Wait, maybe the line of reflection is x=-2? No, (-4 + 0)/2=-2, but the top vertices: left top at (-3,8), right top at (1,8). Midpoint is (-3 + 1)/2=-1. Hmm, conflicting. Wait, maybe the figure is symmetric about x=-1. Wait, the problem is to find the line of reflection. The correct line is x=-1? No, wait, the answer is x=-1? Wait, no, let's look at the original figure. The left triangle: its right edge is at x=-2, and the right triangle's left edge is at x=0. The distance between -2 and 0 is 2, so the midpoint is -1. So the line of reflection is x=-1. Wait, no, maybe the line is x=-1.

Step2: Write the equation

The equation of a vertical line is x = a, where a is the x - coordinate. So the line of reflection is x=-1. Wait, no, wait, the figure: maybe the line is x=-1. Wait, no, let's check again. The two triangles: the left one and the right one, symmetric about x=-1. So the equation is x=-1.

Answer:

x=-1