Given two vectors $a = (1, -1)$ and $b = (m+1, 2m-4)$, if $a$ is perpendicular to $b$, find the value of $m$.

1. Problem Description

Given two vectors $a = (1, -1)$ and $b = (m+1, 2m-4)$, if $a$ is perpendicular to $b$, find the value of $m$.

2. Solution Steps

If two vectors are perpendicular, their dot product is zero. The dot product of $a$ and $b$ is calculated as follows:

$a \cdot b = (1)(m+1) + (-1)(2m-4)$

Since $a \perp b$, we have $a \cdot b = 0$.

Therefore, $(1)(m+1) + (-1)(2m-4) = 0$

$m+1 - 2m + 4 = 0$

$-m + 5 = 0$

$m = 5$

3. Final Answer

The value of $m$ is

5. The correct answer is A. 5.