Question 124
We are given the line $p$ with equation $-x+2y=1$ and the line $q$ with equation $-4x+3y=16$. Let the point $A$ be the intersection of the line $p$ with the $x$-axis, let the point $B$ be the intersection of the line $q$ with the $x$-axis, let the point $C$ be the intersection of the lines $p$ and $q$, and let the point $D$ be the orthogonal projection of the point $C$ onto the $x$-axis.
a) Compute and write down the coordinates of the points $A, B, C$ and $D$.
b) Compute the size of the interior angle $\beta$ in triangle $ABC$.
c) Compute the area of triangle $ABC$.
a) Compute and write down the coordinates of the points $A, B, C$ and $D$.
b) Compute the size of the interior angle $\beta$ in triangle $ABC$.
c) Compute the area of triangle $ABC$.