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maria [59]
2 years ago
6

What is the center of the circle that has a diameter whose endpoints are (9, 7) and (-3, -5)?

Mathematics
2 answers:
Naddika [18.5K]2 years ago
8 0

Answer:

(3, 1)

Step-by-step explanation:

Midpoint of the diameter is the center

Since endpoints are (9, 7) and (-3, -5)

Midpoint will be:

  • ((9 - 3)/2, (7-5)/2) = (3, 1)

So the center is (3, 1)

zmey [24]2 years ago
4 0

Answer:

(3, 1)

Step-by-step explanation:

Midpoint of the diameter is the center

Since endpoints are (9, 7) and (-3, -5)

Midpoint will be:

((9 - 3)/2, (7-5)/2) = (3, 1)

or 3/1, 2/2 = (3,1)

So the center is (3, 1)

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1. Assume O P || NM.
ipn [44]

1. Assuming OP || NM, considering the triangle proportionality theorem possible measurements for the segments are: ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units

2. The possible values are decided by assuming  \frac{ON}{LO} = \frac{PM}{LP} = 3 using the triangle proportionality theorem.

3. Another method is applying the AA Similarity Theorem to compare corresponding side lengths of the triangles that are proportional to each other.

<h3>What is the Triangle Proportionality Theorem?</h3>

Triangle proportionality theorem states that if a line is parallel to one of the sides of a triangle intersects two of the other two sides, it divides the two sides into proportional corresponding segments.

1. Assuming that OP || NM, we would apply the triangle proportionality theorem to have the following ratio:

\frac{ON}{LO} = \frac{PM}{LP}

Using the above ratio, we can choose the following possible lengths for the segments:

ON = 3 units

LO = 1 unit

PM = 6 units

LP = 2 units

2. The values are decided assuming that the ratio, \frac{ON}{LO} = \frac{PM}{LP} = 3

This means that the ratio of the proportional segments, irrespective of the their measurement should give you an assumed equal ratio of 3:1.

Therefore, since:

\frac{3}{1} = 3\\\\\frac{6}{2} = 3

The measurements, ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units are therefore possible measurements.

3. Using the AA Similarity Theorem to prove that ΔLPO ≅ ΔLMN, the corresponding sides of both triangles will be proportional.

LP/LM = LO/LN = PO/MN

We can use this to choose possible measurements while assuming a ratio between the proportional sides of both triangles.

Let's assume that: LP/LM = LO/LN = PO/MN = 1/4

Let,

LO = 1 unit

LN = 4 units

Therefore, ON = LN - LO = 4 - 1 = 3 units.

Same way the other possible measures can be gotten provided a ratio is assumed.

Learn more about triangle proportionality theorem on:

brainly.com/question/24804474

4 0
2 years ago
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