Question

given: prove: statements reasons 1. given 2. application of the slope formula 3. distance from to equals the distance from to definition of parallel lines 4. application of the distance formula 5. substitution property of equality 6. inverse property of addition 7. substitution property of equality which step of the proof contains an error? a. step 6 b. step 5 c. step 4 d. step 2

Answer 1

The correct answer is b.) The step of the proof that contains an error is step 5. In step 5, the error occurs because the substitution property of equality is being applied incorrectly.

Step-by-step explanation:

The step of the proof that contains an error is step 5.

In step 5, the error occurs because the substitution property of equality is being applied incorrectly. The substitution property of equality states that if two quantities are equal, they can be replaced with each other in an equation. However, in this step, the substitution is not valid because the two quantities being replaced are distances, which are not necessarily equal just because they are between parallel lines.

To correct this error, a different reasoning or justification should be provided to show that the distances are equal.

Answer 2

The most likely error in the geometric proof involving the slope and distance formulas is in step 6, the inverse property of addition, as this step may not directly relate to proving properties of parallel lines, unless dealing with vector concepts.

Step-by-step explanation:

Without seeing the full details of the proof question, the provided information seems to reference a geometric proof involving slope and distance formulas. Among the listed steps, the step most likely to contain an error is the application of the inverse property of addition, which is step 6. This is because typically, the inverse property of addition would be used to show that adding the opposite (or inverse) of a number to itself yields zero, which might not be directly relevant to a proof involving distances and slopes unless dealing with vector subtraction or a similar context.

Since step 4 involves the application of the distance formula, it is crucial to ensure that it is applied correctly to compute the distance between two points. If misapplied, this could lead to an erroneous conclusion. Therefore, without specific error details, step 6 seems the most out of place given the provided steps relating to proving properties associated with parallel lines, slope, and distance.