taiwan-gsat 2025 Q7

taiwan-gsat · Other · gsat__math-b 5 marks Curve Sketching Lattice Points and Counting via Graph Geometry
A person uses single-point perspective with a point on the horizon as the vanishing point to draw six vertical pillars $A , B , C , D , E , F$ on a coordinate plane. The coordinates of the top and base of each pillar are shown in the table below, with point $V ( 4,9 )$ representing the vanishing point, as shown in the figure. Since the base line and top line of pillars $A$ and $F$ in the figure are both parallel to the horizon, the actual heights of pillars $A$ and $F$ are equal. Based on the above, select the pillar with the maximum actual height.
Pillar$A$$B$$C$$D$$E$$F$
Top coordinate$( 0,8 )$$( 2,3 )$$( 4,6 )$$( 6,8 )$$( 8,5 )$$( 10,8 )$
Base coordinate$( 0,6 )$$( 2,0 )$$( 4,3 )$$( 6,5 )$$( 8,1 )$$( 10,6 )$

(1) $A$
(2) $B$
(3) $C$
(4) $D$
(5) $E$
A person uses single-point perspective with a point on the horizon as the vanishing point to draw six vertical pillars $A , B , C , D , E , F$ on a coordinate plane. The coordinates of the top and base of each pillar are shown in the table below, with point $V ( 4,9 )$ representing the vanishing point, as shown in the figure.\\
Since the base line and top line of pillars $A$ and $F$ in the figure are both parallel to the horizon, the actual heights of pillars $A$ and $F$ are equal. Based on the above, select the pillar with the maximum actual height.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
Pillar & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ \\
\hline
Top coordinate & $( 0,8 )$ & $( 2,3 )$ & $( 4,6 )$ & $( 6,8 )$ & $( 8,5 )$ & $( 10,8 )$ \\
\hline
Base coordinate & $( 0,6 )$ & $( 2,0 )$ & $( 4,3 )$ & $( 6,5 )$ & $( 8,1 )$ & $( 10,6 )$ \\
\hline
\end{tabular}
\end{center}

(1) $A$\\
(2) $B$\\
(3) $C$\\
(4) $D$\\
(5) $E$