Triangle ABC is defined by the points A(2,9), B(8,4), and ((-3,-2).
Complete the following equation for a line passing through point C and perpendicular AB.

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06-06-2022
Mathematics

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Triangle ABC is defined by the points A(2,9), B(8,4), and ((-3,-2).
Complete the following equation for a line passing through point C and perpendicular AB.

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MaheshpatelvVTidn MaheshpatelvVTidn · Answer 1 · 2022-06-20T13:14:57-04:00

The equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.

What is the slope?

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2).

The slope of the segment AB:

[tex]\rm m =\dfrac{4-9}{8-2}[/tex]

m = -5/6

The slope of the line perpendicular to AB:

Let M is the slope of the line:

mM = -1

(-5/6)M = -1

M = 6/5

The line:

y = Mx + c

y = (6/5)x + c

The line passing through the point C(-3, -2)

-2 = (6/5)(-3) + c

c = 8/5

y = (6/5)x + 8/5

5y = 6x + 8

Thus, the equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.

Learn more about the slope here:

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Sagot :

What is the slope?

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