MCQ
If points $A(5, p), B(1,5), C(2,1)$ and $D(6,2)$ form a square $\ce{ABCD}$, then $p=$
- A7
- B3
- ✓6
- D8
✓
Answer
Correct option: C.
6
Since $\ce{ABCD}$ is a square.
$\therefore A B=A D \Rightarrow A B^2=A D^2$
$\Rightarrow(1-5)^2+(5-p)^2=(6-5)^2+(2-p)^2$
$\Rightarrow 16+25-10 p+p^2=1+4-4 p+p^2$
$\Rightarrow 6 p=36 $
$\Rightarrow p=6$
$\therefore A B=A D \Rightarrow A B^2=A D^2$
$\Rightarrow(1-5)^2+(5-p)^2=(6-5)^2+(2-p)^2$
$\Rightarrow 16+25-10 p+p^2=1+4-4 p+p^2$
$\Rightarrow 6 p=36 $
$\Rightarrow p=6$
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