Q. 105.0( 1 Vote )
Write the coordinates of the image of the point (3, 8) in the line x + 3y – 7 = 0.
Answer :
Given:
Line x + 3y – 7 = 0, point (3, 8).
To find:
The coordinates of the image.
Explanation:
Let the given point be A(3,8) and its image in the line x + 3y − 7 = 0 is B(h,k).
The midpoint of AB is 
that lies on the line x + 3y − 7 = 0.
∴
h + 3k + 13 = 0 … (1)
AB and the line x + 3y − 7 = 0 are perpendicular.
∴Slope of AB × Slope of the line = - 1
⇒ 
⇒ 3h – k – 1 = 0 … (2)
Solving (1) and (2), we get:
(h, k) = (− 1, − 4)
Hence, the image of the point (3,8) in the line x + 3y − 7 = 0 is (− 1, − 4).
Rate this question :
Various Forms of Equations of line45 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Parametric Equations of Straight line48 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 1169 mins
Find what the given equation becomes when the origin is shifted to the point (1, 1).
xy – x – y + 1 = 0
RS Aggarwal - Mathematics
Find what the given equation becomes when the origin is shifted to the point (1, 1).
x2 – y2 – 2x + 2y = 0
RS Aggarwal - Mathematics
At what point must the origin be shifted, if the coordinates of a point (-4,2) become (3, -2)?
RS Aggarwal - MathematicsWrite the coordinates of the image of the point (3, 8) in the line x + 3y – 7 = 0.
RD Sharma - MathematicsIf the origin is shifted to the point (2, -1) by a translation of the axes, the coordinates of a point become (-3, 5). Find the origin coordinates of the point.
RS Aggarwal - MathematicsIf the origin is shifted to the point (0, -2) by a translation of the axes, the coordinates of a point become (3, 2). Find the original coordinates of the point.
RS Aggarwal - MathematicsIf the origin is shifted to the point (1, 2) by a translation of the axes, find the new coordinates of the point (3, -4).
RS Aggarwal - MathematicsFind what the given equation becomes when the origin is shifted to the point (1, 1).
xy – y2 – x + y = 0
RS Aggarwal - Mathematics
