On a coordinate plane, point B(–6, 1) is translated to B prime(–3, –2). Indira uses these steps to find a rule to describe the translation.
Step 1 Substitute the original coordinates and the translated coordinates into (x, y) right-arrow (x + a, y + b):
B (negative 6, 1) right-arrow B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2)
Step 2
Write two equations:
Negative 6 + a = negative 2. 1 + b = negative 3.
Step 3
Solve each equation:
Negative 6 + a = negative 2. a = negative 2 + 6. a = 4. 1 + b = 3. b = negative 3 minus 1. b = negative 4.
Step 4
Write the translation rule:
(x, y) right-arrow (x + 4, y minus 4)
Which corrects Indira’s first error?
Indira should have substituted B (negative 6, 1) right-arrow B prime (negative 3 + a, negative 2 + b) = B prime (negative 6, 1) in Step 1.
Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.
Indira should have solved the equations to find that a = negative 8 and b = negative 2 in Step 3.
Indira should have written the translation rule (x, y) right-arrow (x minus 4, y + 4) in Step 4.