Question

A point (x + 2, x + 4) lies in the first quadrant, the mirror image for which for x-axis is (5, –7). What is the value of x?
a) (–5, –7)
b) (–5, 7)
c) (5, –7)
d) (5, 7)​

Answer 1

Answer

3+2 , 3-10

So your answer is

5,-7

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

We know,

If a point is in the first quadrant, reflected under x - axis,

then

the image lies in the fourth quadrant,

So,

reflection of point (x, y) is (x, - y) under the x-axis.

Now,

$\bigstar \: \: \red{ \rm \: According \: to \: statement }$

$\rm \: \rightarrow \ The \: point \: (x+2,x+4) \: lies \: in \: {1}^{st} \: quadrant.$

So,

Its mirror image under x - axis lies in 4th quadrant.

$\rm \: \rightarrow \: So, \: its \: mirror \: image \: is \: (x+2, \: - \: x - 4)$

Now,

$\bigstar \: \: \red{ \rm \: According \: to \: statement }$

$\rm \: \rightarrow \: The \: mirror \: image \: of \: (x+2,x+4) \: \: is \: (5, \: - 7)$

So, on comparing we get,

$\rm : \implies \:x + 2 = 5$

$\bigstar \: \: \boxed{ \pink{ \rm : \implies \:x \: = \: 3}}$

$\bigstar \: \: \boxed{ \pink{ \rm : \implies Hence, \: the \: coordinates \: is \: (5, \: 7)}}$

$\rm : \implies \: \large\boxed{ \red{ \bf \: option \: (d) \: is \: correct}}$