How to solve this Algebra question?

Mathematics

1 answer:

PIT_PIT [208]2 years ago

7 0

Slope formula: $\frac{y_2-y_1}{x_2-x_1}$

Firstly, let's set up our equation. Place the two coordinates in the slope formula and have it equal 8: $\frac{3k-4-k}{5-(-2)}=8$

Next, combine like terms: $\frac{2k-4}{7}=8$

Next, multiply both sides by 7: $2k-4=56$

Next, add 4 onto both sides of the equation: $2k=60$

Lastly, divide both sides by 2 and <u>your answer will be $k=30$ </u>

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It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

<h3>How to prove a Line Segment?</h3>

We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.

Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.

In ΔPNM, ∠N = 90°

∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)

∠P + ∠M = 90°

Clearly, ∠M is an acute angle.

Thus; ∠M < ∠N

PN < PM (The side opposite to the smaller angle is smaller)

Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

Read more about Line segment at; brainly.com/question/2437195

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