The given triangle has points A(1, 2), B(3, 5), and C(2, 7)
When the triangle is translated by the rule (-5, -6), the new points of the triangle becomes:
A'(1-5, 2-6) = A'(-4, -4)
B'(3-5, 5-6) = B'(-2, -1)
C'(2-5, 7-6) = C'(-3, 1)
Summarily, the points after translation of the triangle by the rule (-5, -6) are A'(-4, -4), B'(-2, -1), C'(-3, 1)
Then the triangle is reflected over the y-axis:
When a triangle is reflected over the y-axis, the coordinates of the y-axis remains the same, but the coordinates of the x-axis is negated.
The new points ofthe triangle after reflection therefore become:
A''(4, -4), B''(2, -1), C''(3, 1)
The three triangles(that is, the original, after translation, and after reflection) are plotted below
