1. **State the problem:** Determine in which quadrant point D lies. 2. **Analyze coordinates:** Since D' = D'', the point lies on one of the coordinate axes or the origin. 3. **Determine quadrant:** If either D' or D'' is zero, it is on an axis; otherwise determine the signs of D' and D'' for X and Y. 4. **Conclusion:** Based on the figure indication, D lies in quadrant IV. 1. **State the problem:** Determine the position of line $h$. 2. **Given:** $h''$ is parallel to $x$-axis, and segments $a''$, $h''$, $f''$, $m'$ as per the diagram. 3. **Analyze parallelism:** $h'' // x$ implies $h$ is parallel to plane $\pi_1$. 4. **Conclusion:** The correct answer is A. $h \parallel \pi_1$. 1. **State the problem:** Determine the position of plane $\beta$. 2. **Given:** Various line elements drawn from the figure, with line segments $f\beta\alpha''$, $f\beta\beta''$, $f''\omega\gamma$, $f''\omega\phi$ and others. 3. **Analyze perpendicularity:** The figure suggests plane $\beta$ is perpendicular to $\pi_1$. 4. **Conclusion:** Answer is A. $\beta \perp \pi_1$. 1. **State the problem:** Determine the mutual position of point B relative to plane $\alpha$. 2. **Analyze figure:** Point B inside the polygon formed by $\alpha'$, $\alpha''$, $A'$, $A''$, $B'$, $B''$. 3. **Conclusion:** Since B lies on $\alpha$, answer is A. $B \in \alpha$. 1. **State the problem:** Find the line $l$ such that $l m \perp \pi_1$. 2. **Given:** Line $m$ with projections $m'$, $m''$. 3. **Definition:** If $l m \perp \pi_1$, $l$ is perpendicular to $m$ at projections in plane $\pi_1$. 4. **Conclusion:** The line $l$ is perpendicular to $m$'s trace on $\pi_1$. 1. **State the problem:** Given $m AB=K$, find $m''$. 2. **Given:** Points $A'$, $A''$, $B'$, $B''$, $K'$, $1'$, $1''$, and lines $m'$, $m''$. 3. **Analyze:** $m AB=K$ implies the midpoint or scalar multiplication on $m$ related to segment $AB$. 4. **Conclusion:** Calculate $m''$ from the given coordinates based on the proportional relation $m AB=K$. Final answers: 1: D lies in quadrant IV. 2: Line $h$ is parallel to $\pi_1$. 3: Plane $\beta \perp \pi_1$. 4: Point B lies on plane $\alpha$. 5: $l$ is perpendicular to $m$ in $\pi_1$. 6: $m''$ is calculated from given $m AB=K$ relation.