Question

If $A(-2,-1),B(4,0),C(3,3)$ and $D(-3,2)$ are the vertices of a parallelogram, then
Statement I Slope of $AB=$ Slope of $BC$ and
Slope of $CD=$ Slope of $AD$.
Statement II Mid-point of $AC=$ Mid- point of $BD$.

• A. Both statements are true
• B. Statement I is true and Statement II is false
• C. Statement I is false and Statement II is true
• D. Both statements are false

Answer 1

Answer: (C)

$\because ABCD$ is a parallelogram.
$\therefore AB\Vert CD\Rightarrow$ Slope of $AB=$ Slope of $CD$
and $BC\Vert AD\to$ Slope of $BC=$ Slope of $AD$
Hence, Statement $I$ is false.
Now, mid-point of $AC=\left(\frac{-2+3}{2},\frac{-1+3}{2}\right)$
$=\left(\frac{1}{2},\frac{2}{2}\right)=\left(\frac{1}{2},1\right)$
and mid-point of $BD=\left(\frac{4-3}{2},\frac{0+2}{2}\right)=\left(\frac{1}{2},1\right)$
$\Rightarrow$ Mid-point of $AC=$ Mid-point of $BD$
Hence, Statement II is true.