Question

4. Line r is mapped onto line m by a dilation centered at the origin with a

scale factor of 4. The equation of line r is 6x – 3y = 12. What is the
equation for line m?

Answer 1

3x - y = 8

Explanation:

Since, if a line having points represented by (x,y) is dilated about origin with a scale factor k,

Then the coordinates of the dilated line is obtained by the rule,

Here, line L is,

3x - y = 4

The x-intercept and y-intercept of line L are (4/3,0) and (0,-4) respectively,

If the line L is mapped onto line M by a dilation centered at the origin with a scale factor of 2,

Then by the above definition,

The points of the line M are,

(2×4/3, 2×0) and (2×0, 2×-4) ⇒ (8/3,0) and (0,-8)

Hence, the equation of line M passes through the points (8/3,0) and (0,-8)