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Nezavi [6.7K]
1 year ago
10

To find the angle of rotation θ between the previous x and y axes and the new x′ and y′ axes, we use the formula: cotangent of 2

theta equals A minus C all over B , where 2θ lies on the interval (0°, 180°).TrueFalse

Mathematics
1 answer:
Tamiku [17]1 year ago
7 0

The equation is the given one:

\cot 2\theta=\frac{A-C}{B}

Which is the same as:

\tan 2\theta=\frac{B}{A-C}

And the interval of the angle θ must be (0°,90°) so, 2θ must be (0°,180°).

So the statement is True.

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Find the midpoint M of the line segment joining the points C = (-1, -1) and D = (5, -5). ​
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Answer:

The midpoint between the joining points C and D is (2, -3)

Step-by-step explanation:

How to find a midpoint

  • 1: Label the coordinates(x₁,y₁) and (x₂,y₂).
  • 2: Input the values into the formula.
  • 3: Add the values in the parentheses and divide each result by 2.
  • 4: The new values form the new coordinates of the midpoint.

Suppose we have a line segment and want to cut that section into two equal parts. To do so, we need to know the center. We can achieve this by finding the midpoint. You could measure with a ruler or just use a formula involving the coordinates of each endpoint of the segment. The midpoint is simply the average of each coordinate of the section, forming a new coordinate point. We shall illustrate this below.

Midpoint formula

If we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. This forms a new coordinate you can call (x₃,y₃).  It is possible to divide a line segment into any given ratio, not just 1:1.

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