A point P(x + 2, x + 4) lies in the first quadrant, the mirror image f

1.	A point P(x + 2, x + 4) lies in the first quadrant, the mirror image for which for x-axis is Q(5, –7). Find the value of x and then find what will be the coordinates of the point P? a) (–5, –7) b) (–5, 7) c) (5, –7) d) (5, 7
Answer» ✪ᴀɴsᴡᴇʀ✪ $\pink{\large{\boxed{\bf{x = 3, \: <klux>P</klux> = (<klux>5</klux>, 7)}}}}$ ★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★ It is given that mirror image of P(x+2, x+4) about x-axis is Q(5, - 7). When a point is REFLECTED about x-axis, its x co-ordinate REMAINS unchanged but its y co-ordinate becomes OPPOSITE in sign. So, $\to (x+2, - (x+4)) = (5, - 7)$ $\to x+2 = 5, - (x+4)= - 7$ $\to x = 3, x +4 = 7$ $\to x = 3, x = 3$ $\to x = 3$ And, co-ordinate of P are $\to (x+2, x+4)$ $\to (3+2, 3+4)$ $\to (5, 7)$