Question

solve it.please
$if \: points \: \: a(5.p) \: \: b(1.5) \: c(6.2)and \: d(6.2) \: form \: a \: square \: abcd \: then \: p = \\ \\ \\ (a)7 \\ (b)3 \\ (c)6 \\ (d)8$
the question is from 10 th coordinate geometry.......

answer with step_by_step explaination..​

Answer 1

hey mate

here is your answer in the pic

Answer 2

$\large \pink{ \textbf{side \: a \: and \: b \: should \: be \: }} \\ \large \pink{ \text{equal \: to \: side \: c \: and \: d \: now}} \\ \\ a(5,p) \: \: \: b(1,5) \: \: c(6,2) \: \: d(6,2) \\ \\ \sqrt{ ({y2}^{2} - {y1}^{2} ) + ({x2}^{2} - {x1}^{2}) } \\ \\ = \sqrt{25 - {p}^{2} + 1 - 25 } = \sqrt{1 - {p}^{2} } \\ \\ from \: c,d \: we \: have : \\ \\ \sqrt{ ({y2}^{2} - {y1}^{2} ) + ({x2}^{2} - {x1}^{2}) } \\ \\ = \sqrt{4 - 4 + 36 - 36 } = 0 \\ \\ now.. \\ \\ \sqrt{1 - {p}^{2} } = 0 \\ \\ 1 - {p}^{2} = 0 \\ \\ {p}^{2} = 1 \\ \\ p = \sqrt{1} = 1$