The point (4, 1) undergoes the following two successive transformations: (i) Reflection about the line y = x. (ii) Translation through a distance of 2 units along the positive x-axis. Then the final coordinates of the point are

Question

The point (4, 1) undergoes the following two successive transformations: (i) Reflection about the line y = x. (ii) Translation through a distance of 2 units along the positive x-axis. Then the final coordinates of the point are (A) (4, 3) (B) (3, 4) (C) (1, 4) (D) ((7/2), (7/2))

Tardigrade Admin · Accepted Answer

The image of the point (4, 1) after reflection about the line y = x is (1,4). And then translation through a distance of 2 units along positive x-axis. ∴ Final position of a point is (1 + 2,4) i.e., (3,4).

Q. The point $(4, 1)$ undergoes the following two successive transformations :
(i) Reflection about the line $y = x$ .
(ii) Translation through a distance of $2$ units along the positive $x$ -axis.
Then the final coordinates of the point are

$(4, 3)$

$(3, 4)$

$(1, 4)$

$(\frac{7}{2}, \frac{7}{2})$

The image of the point $(4, 1)$ after reflection about the line $y = x$ is $(1, 4)$ .
And then translation through a distance of $2$ units along positive $x$ -axis.
$∴$ Final position of a point is $(1 + 2, 4)$ i.e., $(3, 4)$ .

Q. The point (4,1) undergoes the following two successive transformations : (i) Reflection about the line y=x. (ii) Translation through a distance of 2 units along the positive x-axis. Then the final coordinates of the point are

(4,3)

(3,4)

(1,4)

(27​,27​)