Find the values of m and n, in each case; if :

(i) (4, -3) on reflection in x-axis gives (-m, n).

(ii) (m, 5) on reflection in y-axis gives (-5, n - 2)

(iii) (-6, n + 2) on reflection in origin gives (m + 3, -4).

(i) We know that,

On reflection in x-axis, the sign of y-coordinate changes.

∴ (4, -3) on reflection in x-axis gives (4, 3).

Given,

(4, -3) on reflection in x-axis gives (-m, n)

∴ (-m, n) = (4, 3)

⇒ -m = 4 and n = 3

⇒ m = -4 and n = 3.

Hence, m = -4 and n = 3.

(ii) We know that,

On reflection in y-axis, the sign of x-coordinate changes.

∴ (m, 5) on reflection in y-axis gives (-m, 5).

Given,

(m, 5) on reflection in y-axis gives (-5, n - 2)

∴ (-m, 5) = (-5, n - 2)

⇒ -m = -5 and n - 2 = 5

⇒ m = 5 and n = 7.

Hence, m = 5 and n = 7.

(iii) We know that,

On reflection in origin, the sign of x-coordinate and y-coordinate changes.

∴ (-6, n + 2) on reflection in origin gives [6, -(n + 2)].

Given,

(-6, n + 2) on reflection in origin gives (m + 3, -4)

∴ [6, -(n + 2)] = (m + 3, -4)

⇒ 6 = m + 3 and -(n + 2) = -4

⇒ m = 6 - 3 and -n - 2 = -4

⇒ m = 3 and -n = -4 + 2

⇒ m = 3 and -n = -2

⇒ m = 3 nd n = 2.

Hence, m = 3 and n = 2.