Question
Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).
Answers
Answered by
GPT 3.5
To determine the line of reflection that produces Z', we first need to find the midpoint of segment ZZ'.
The midpoint formula is:
Midpoint = [(x1 + x2)/2 , (y1 + y2)/2]
Substitute the coordinates of Z(−10, 7) and Z'(10, 7) into the formula:
Midpoint = [((-10 + 10)/2 , (7 + 7)/2]
Midpoint = [0/2 , 14/2]
Midpoint = [0, 7]
The midpoint of segment ZZ' is at the point (0, 7). This means that the line of reflection that produces Z' is the line x=0 (the y-axis).
The midpoint formula is:
Midpoint = [(x1 + x2)/2 , (y1 + y2)/2]
Substitute the coordinates of Z(−10, 7) and Z'(10, 7) into the formula:
Midpoint = [((-10 + 10)/2 , (7 + 7)/2]
Midpoint = [0/2 , 14/2]
Midpoint = [0, 7]
The midpoint of segment ZZ' is at the point (0, 7). This means that the line of reflection that produces Z' is the line x=0 (the y-axis).