Question

Four students are trying to find the rule that translates point N(–2, –4) to N prime (2, 4). Each student’s reasoning is shown below. Raheem: The rule is (x times (negative 1), y times (negative 1)) because Negative 2 times (negative 1) = 2 and Negative 4 times (negative 1) = 4. Casey: The rule is (x 2, y 4) because the image is (2, 4). Andrew: The rule is (x 4, y 0) because the coordinates are opposites. Lo: The rule is (x 4, y 8) because Negative 2 4 = 2 and Negative 4 8 = 4. Which student is correct? Raheem Casey Andrew Lo.

Answer 1

Four students are trying to find the rule that translates point N (–2, –4) to N prime (2, 4),

According to Lo's statement : The rule is (x + 4, y + 8) because Negative 2 + 4 = 2 and Negative 4 + 8 = 4.

The answer of Lo is Correct By applying the rule (x+4, y+8) on the coordinates N(-2, -4) will give us N'(2,4)

How do find whose statement is correct?

To find that we need to first understand students' statements accordingly.

Given: Student statements as:-

• Raheem: The rule is (x times (negative 1), y times (negative 1)) because Negative 2 times (negative 1) = 2 and Negative 4 times (negative 1) = 4.

• Casey: The rule is (x + 2, y + 4) because the image is (2, 4).

• Andrew: The rule is (x + 4, y + 0) because the coordinates are opposites.

• Lo: The rule is (x + 4, y + 8) because Negative 2 + 4 = 2 and Negative 4 + 8 = 4.

Now let's understand all the statements of respective students,

According to Raheem, his statement is incorrect because it states that we can only use addition or subtraction and not multiplication in transitions.

Therefore, Raheem's answer is NOT CORRECT.

According to Casey, his statement is incorrect because after applying the rule : (x+2, y+4) on the coordinates N(-2, -4) that will give (0,0) but not N'(2,4).

Therefore, Casey's answer is NOT CORRECT.

According to Andrew, his statement is incorrect because after applying the rule: (x+4, y+0) on the coordinates N(-2, -4) that will give us (2,-4) but not N'(2,4).

Therefore, Andrew's answer is NOT CORRECT.

According to Lo, his statement is correct because after applying the rule: (x+4, y+8) on the coordinates N(-2, -4) that will give us N'(2,4).

Therefore, Andrew's answer is CORRECT.

Hence, The answer of Lo is Correct By applying the rule (x+4, y+8) on the coordinates N(-2, -4) will give us N'(2,4)

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