Question

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.

Answer 1

Answer:

Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.

Step-by-step explanation:

point B(–6, 1)  goes to B prime(–3, –2)

-6 goes to -3  which means we add 3

1 goes to -2  which means we subtract 3

x+a = x'       y+b = y'

-6+a = -3     1 + b = -2

Add 6            Subtract 1

a = -3+6          b = -2-1

a = +3            b = -3

Answer 2

Answer:

Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.

Step-by-step explanation:

Point B(-6, 1) to B'(-3, -2)

Steps to achieve B"

-6+a= -3 ⇒ a= -3+6= 3

1+b= -2 ⇒ b= -2-1= -3

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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.
• wrong step

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)

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• Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.