Coordinate Geometry
Triangles
MMTS_Full_Test_04
Grade 12
Question:
In $\triangle ABC$, $AB=AC$ where $A=(3,1)$ and the equation of the base $BC$ is $2x+y=4$. Also $B$ lies on $x+3y=7$. Then sum of coordinates of vertex $C$ is
$\dfrac{13}{5}$
$\dfrac{18}{5}$
$\dfrac{16}{5}$
$\dfrac{7}{5}$
Step-by-Step Solution
Key Concept: $AB=AC$: $A$ lies on perpendicular bisector of $BC$
$B$: intersection of $2x+y=4$ and $x+3y=7$: $B=(1,2)$. Since $AB=AC$ and $A=(3,1)$: $C$ is reflection of $B$ about the altitude from $A$... Sum of coordinates of $C=18/5$.
Correct Answer: 2