Determine whether the statement is true or false.

The lines with equation ax+by+c1=0 and bx-ay+c2=0, where a ≠ 0 and b≠ 0, are perpendicular to each other.
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True. The slopes of the lines are m1 and m2 respectively; m1=b/a, m2=-a/b, so m1=-1/m2.

or

False. The slopes of the lines are m1 and m2 respectively; m1=-b/a, m2=-a/b, so m1=1/m2.

True.

m1 = -a/b
m2 = b/a

False. The slopes of the lines are m1 and m2 respectively; m1=-b/a, m2=-a/b, so m1 does not equal 1/m2. Therefore, the lines are not perpendicular to each other.

True. To determine whether two lines are perpendicular to each other, we need to compare their slopes. The slopes of the lines can be determined from their given equations.

For the first line, ax + by + c1 = 0, we rearrange it to the slope-intercept form, y = -(a/b)x - c1/b. From this form, we can see that the slope of the first line is -a/b.

For the second line, bx - ay + c2 = 0, we rearrange it to the slope-intercept form, y = (b/a)x + c2/a. From this form, we can see that the slope of the second line is b/a.

Since a and b are both non-zero, we can conclude that these equations are valid.

Now, let's compare the slopes of the two lines:

m1 (slope of the first line) = -a/b
m2 (slope of the second line) = b/a

To determine if the lines are perpendicular, we need to check if m1 is equal to -1/m2.

If m1 is equal to -1/m2, then the lines are perpendicular.

In this case, m1 = -a/b, and -1/m2 = -1/(b/a) = -a/b.

Since m1 = -1/m2, we can conclude that the lines with equations ax + by + c1 = 0 and bx - ay + c2 = 0 (where a ≠ 0 and b ≠ 0) are indeed perpendicular to each other.

Therefore, the statement is true.