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kvasek [131]
2 years ago
14

What is the slope of the line that passes through the points (-6, 8)and (-9, 7)?

Mathematics
1 answer:
Effectus [21]2 years ago
7 0

Answer:

m= 1/3

Step-by-step explanation:

m = \frac{y2 - y1}{x2 - x1}

   = \frac{7 - 8}{-9 - (-6)} = \frac{-1}{-9 + 6} = \frac{-1}{-3} = \frac{1}{3}

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So,

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<img src="https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Ctext%7Bquestion%7D%7D%7D%20%3A%20" id="TexFormula1"
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Answer:

See Below.

Step-by-step explanation:

In the given figure, AP = BP = PC.

And we want to prove that ∠ABC is a right angle.

Since AP = BP and BP = PC, we can create two isosceles triangles: ΔAPB and ΔCPB.

By the definition of isosceles triangles, in ΔAPB, ∠PAB and ∠PBA are equivalent. Let the measure of each of them be <em>x°</em>.

Likewise, in ΔCPB, ∠PCB and ∠PBC are equivalent.

And since AP = BP = PC, each of the angles∠PCB and ∠PBC will also be equivalent to <em>x°.</em>

<em />

And since the sum of the interior angles of a triangle total 180°, we acquire:

\angle PAB+\angle PBA+\angle PCB+\angle PBC=180

Since they are all equivalent:

4x=180

Hence:

x=45^\circ

∠ABC is the sum of ∠PBA and ∠PBC, each of which measures 45°. Hence:

\angle ABC=\angle PBA+\angle PBC=45+45=90^\circ

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