Respuesta :
Answer: 3x - y = 8
Step-by-step 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,
[tex](x,y)\rightarrow (kx,ky)[/tex]
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)
[tex]y+0=\frac{-8-0}{0-8/3} (x-\frac{8}{3})[/tex]
[tex]\implies y = 3(\frac{3x-8}{3})[/tex]
[tex]\implies 3y=3(3x-8)[/tex]
[tex]\implies y = 3x - 8[/tex]
[tex]\implies 3x - y = 8[/tex]
Answer:
Equation of the line M is [tex]2y=6x-8[/tex] i.e. [tex]y=3x-4[/tex]
Step-by-step explanation:
We are given that,
Line L is mapped onto the line M by a dilation at the origin by a scale factor of 2.
Now, the equation of the line L is [tex]3x-y=4[/tex] i.e. [tex]y=3x-4[/tex].
As, the scale factor of dilation is 2.
Also, dilation only changes the size of the figure and have no other impact.
Thus, the equation of M will be same as that of L but increased in size.
The equation of line M will be [tex]2y=2(3x-4)[/tex] i.e. [tex]2y=6x-8[/tex].
Hence, equation of the line M is [tex]2y=6x-8[/tex].
