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notka56 [123]
3 years ago
12

Use the midpoint formula to find the midpoint between H(3, 9) and J(9, -2).

Mathematics
1 answer:
TiliK225 [7]3 years ago
3 0

Hello!

The midpoint formula is basically an average of x and y.

It is also written as: (\frac{x_{1}+x_{2}} {2},\frac{y_{1}+ y_{2}} {2}).

With the formula above, we can substitute the given points into the equation, and simplify.

(\frac{3 +9}{2}, \frac{9+(-2)}{2}) = (\frac{12}{2}, \frac{7}{2}) = (6, 3.5)

Therefore, the midpoint between points H and J is choice D, (6, 3.5).

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Answer:

  • <em><u>5.6875 in</u></em>

Explanation:

At the point of tangency, the <em>tangent </em>to a circle and the <em>radius</em> form a right triangle (the radius is perpendicular to the tangent).

Here you are given the length of the tangent (6in), and the distance from the bisected vertex to the circle (2.75 in)

I tried to upload the drawing but the tool is not allowing it now.

In the figure:

  • The length of the tangent (6 in) is one leg of the triangle
  • The distance from vertex and the circle (2.75in)  along with the radius forms the hypotenuse of the right triangle: 2.75 + r.
  • The other leg is the radius, r.

Then, you can use Pythagorean theorem:

  • (r)² + (6)² = (r +2.75)²

Solve:

  • r² + 36 =  r² + 5.5r + 7.5625
  • 5.5r = 36 - 7.5625
  • 5.5r = 28.4375
  • r = 5.6875

The solution is in inches: r = 5.6875 inches ← answer

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