Question

The point P (2, −7) is reflected in the point (0, 3); the co-ordinates of the image of point P are ______.

Options

• (2, 13)

• (2, −13)

• (−2, −13)

• (−2, 13)

Answer 1

The point P (2, −7) is reflected in the point (0, 3); the co-ordinates of the image of point P are (−2, 13).

Explanation: 

Let point P on reflection in the point (0, 3) becomes P'(x, y).

So, (0, 3) will be the mid-point of PP'.

By formula,

Mid-point = `((x_1+x_2)/2, (y_1+y_2)/2)`

Substituting values we get:

⇒ (0, 3) = `((2 + x)/2, (-7 +y)/2)`

⇒ `0 = (2+x)/2​ and 3 = (−7+y​)/2`

⇒ 2  + x = 0 and −7 + y = 6

⇒ x = −2 and y = 6 + 7

⇒ x = −2 and y = 13

P' = (−2, 13)