Q. 375.0( 1 Vote )

# The point (4, 1) undergoes the following two successive transformations:(i)Reflection about the line y = x(ii)Translation through a distance 2 units along the positive x-axisThen the final coordinates of the point areA. (4, 3)B. (3, 4)C. (1, 4)D. Let Q(x, y) be the reflection of P(4, 1) about the line y = x, then midpoint of PQ which lies on y = x 4 + x = 1 + y

x – y + 3 = 0 …(i)

Now, we find the slope of given equation y = x

Since, this equation is in y = mx + b form.

So, the slope = m = 1

Slope of PQ = Since, PQ is perpendicular to y = x

And we know that, when two lines are perpendicular then

m1 m2 = -1 y – 1 = - (x – 4)

y – 1 = - x + 4

x + y – 5 = 0 …(ii)

On adding eq. (i) and (ii), we get

x – y + 3 + x + y – 5 = 0

2x – 2 = 0

x – 1 = 0

x = 1

Putting the value of x = 1 in eq. (i), we get

1 – y + 3 = 0

-y + 4 = 0

y = 4

Given that translation through a distance 2 units along the positive x-axis

The point after translation is (1 + 2, 4) = (3, 4)

Hence, the correct option is (b)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Various Forms of Equations of line45 mins  Parametric Equations of Straight line48 mins  Straight line | Analyse your learning through quiz56 mins  Slope, inclination and angle between two lines48 mins  Interactive Quiz on Equations of line23 mins  General Equation of a line43 mins  Motion in a Straight Line - 0372 mins  Motion in a Straight Line - 0665 mins  Motion in a Straight Line - 0556 mins  Motion in a Straight Line - 0261 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 