Question

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 1

✪ᴀɴsᴡᴇʀ✪

• $\pink{\large{\boxed{\bf{x = 3, \: P = (5, 7)}}}}$

★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

$\to (x+2, x+4)$

$\to (3+2, 3+4)$

$\to (5, 7)$