NIMCET 2025 Paper

Let the line $\frac{\mathit{x}}{4}+\frac{\mathit{y}}{2}=1$ meet the $\mathit{x}$-axis and $\mathit{y}$-axis at $\mathit{A}$ and $\mathit{B}$, respectively. $\mathit{M}$ is the midpoint of side $\mathit{A}\mathit{B}$, and ${\mathit{M}}^{\prime }$ is the image of the point $\mathit{M}$ across the line $\mathit{x}+\mathit{y}=1$. Let the point $\mathit{P}$ lie on the line $\mathit{x}+\mathit{y}=1$ such that the $△\mathit{A}\mathit{B}\mathit{P}$ is an isosceles triangle with $\mathit{A}\mathit{P}=\mathit{B}\mathit{P}$. Then the distance between ${\mathit{M}}^{\prime }$ and $\mathit{P}$ is: