Question

Let L denote the line in the xy plane with x and y
intercepts as 3 and 1 respectively Then the image of
the point (-1,-4) in this line is​

Answer 1

Given info : Let L denote the line in the xy plane with x and y intercepts as 3 and 1 respectively.

To find : the image of the points in this line is ...

solution : equation of line is given by,

x/3 + y/1 = 1

⇒x + 3y = 3

Now let (a, b) is the image of point (-1, -4) in this line.

so, midpoint of (a, b) and (-1, -4) lies on the line.

i.e., [(a -1)/2, (b - 4)/2] lies on the line.

so, (a - 1)/2 + 3(b - 4)/2 = 3

⇒a - 1 + 3b - 12 = 6

⇒a + 3b = 19 ........(1)

Slope of line × slope of (a, b) and (-1, -4) = -1

⇒-1/3 × (b + 4)/(a + 1) = -1

⇒b + 4 = 3a + 3

⇒3a - b = 1 ........(2)

From equations (1) and (2) we get,

a = 11/5 and b = 33/5 - 1 = 28/5

Therefore the image of point (-1,-4) on this line is (11/5, 28/5)