Question

Find the value of x and match the following.

• A. -1
• B. 7
• C. 2

Answer 1

In the given line segment, both end points have the same ordinates.
$\therefore$ The ordinate of C is also 2.
$\Rightarrow x=2$


From the given figure, AB = AC
$\Rightarrow A{B}^2=A{C}^2\Rightarrow (2-1{)}^2+(0-3{)}^2=(2-(-1){)}^2+(0-x{)}^2$
$\Rightarrow x=\pm 1$


The diagonals of parallelogram bisect each other.
So, the coordinates of the midpoint of AC = coordinates of the midpoint of BD.
ie.,$(\frac{6+9}{2},\frac{1+4}{2})=(\frac{8+x}{2},\frac{2+3}{2})$
$⟹(\frac{15}{2},\frac{5}{2})=(\frac{8+x}{2},\frac{5}{2})$
$⟹\frac{15}{2}=\frac{8+x}{2}$
$⟹x=7$