Line L is mapped onto line m by a dilation centered at the origin with a scale factor of 2/5. Line m is represented by y=2x+10 a

Question

3 years ago

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Line L is mapped onto line m by a dilation centered at the origin with a scale factor of 2/5. Line m is represented by y=2x+10 a

nd it passes through the point (1, 12). Which of the following is true about line L?
Line L is parallel to m line
Line L is perpendicular to line m
Line L passes through the origin
Line L is the same as line m

Mathematics

2 answers:

Alinara [238K] · Answer 1 · 2022-06-10T11:44:18+03:00

Dilating a line changes the size of the line.

The true statement is (c) Line L passes through the origin

The scale of dilation is given as:

$\mathbf{k = \frac 25}$

The scale represents the slope of line L.

The equation of line M is:

$\mathbf{y = 2x + 10}$

From the above equation, the slope of line M is:

$\mathbf{m = 2}$

The two lines do not have the same slope.

This means that, the lines are not parallel and they are not the same line.

For the two lines to be perpendicular, then the relationship between their slopes is:

$\mathbf{m = -\frac 1k}$

The above is false, because:

$\mathbf{2 \ne -\frac 52}$

Hence, the true statement is (c) Line L passes through the origin