Find the distance between the points (-16, 10) and (-4, -6)

Answer 1

To find the distance between the points \((-16, 10)\) and \((-4, -6)\), we can use the distance formula, which is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

In this case:

• \((x_1, y_1) = (-16, 10)\)
• \((x_2, y_2) = (-4, -6)\)

Now, we can plug in the values:

1. Calculate \(x_2 - x_1\): \[ x_2 - x_1 = -4 - (-16) = -4 + 16 = 12 \]

2. Calculate \(y_2 - y_1\): \[ y_2 - y_1 = -6 - 10 = -16 \]

3. Now substitute these into the distance formula: \[ d = \sqrt{(12)^2 + (-16)^2} \]

4. Calculate \(12^2\) and \((-16)^2\): \[ 12^2 = 144 \] \[ (-16)^2 = 256 \]

5. Combine these results: \[ d = \sqrt{144 + 256} = \sqrt{400} \]

6. Finally, take the square root: \[ d = 20 \]

Therefore, the distance between the points \((-16, 10)\) and \((-4, -6)\) is \(\boxed{20}\).

Answer 2

Which angles are complementary to each other?

Remember, complementary angles add up to 90 degrees

<3 and <5
<3 and <2
<3 and <1
<2 and <5

Answer 3

To determine which pairs of angles are complementary, we should check if the sum of each pair of angles equals 90 degrees. However, since you haven't provided the measures of the angles \(\angle 1\), \(\angle 2\), \(\angle 3\), \(\angle 5\), or if they're given in a specific diagram, I cannot calculate or compare them directly.

If you provide the measures of the angles or any additional context (like a diagram involving the angles), I can assist you in determining which angles are complementary. Otherwise, in general:

• If the sum of the measures of two angles equals 90 degrees, then they are complementary.
• For example, if \(\angle 3\) is 30 degrees and \(\angle 5\) is 60 degrees, since \(30 + 60 = 90\), then \(\angle 3\) and \(\angle 5\) are complementary.

Please provide the angle measures or additional information to proceed!