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4 years ago

Please help with geometry homework ! Mark brainliest

Mathematics

1 answer:

Vika [28.1K]4 years ago

5 0

Theorem: If a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the length of the tangent equals the product of the length of the secant with the length of its external segment.

In your case this theorem sounds as

$6^2=3\cdot x.$

Find x:

$x=\dfrac{6^2}{3}=\dfrac{36}{3}=12.$

Answer: correct choice is C.

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What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

frosja888 [35]

Complete Question:

The given line segment has a midpoint at (3, 1). On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, -2).

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

Answer:

$y = \frac{1}{3}x$

Step-by-step explanation:

From the question, we understand that the line goes through $(2, 4), (3, 1), and\ (4, -2).$

First, we calculate the slope of the above points

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (2,4)$

$(x_2,y_2) = (3,1)$

$m = \frac{1 - 4}{3 - 2}$

$m = \frac{-3}{1}$

$m = -3$

Also; from the question, we understand that the line segment is perpendicular to the above points.

This slope (m2) of the line segment is calculated as:

$m_2 = -\frac{1}{m}$

Substitute -3 for m

$m_2 = -\frac{1}{-3}$

$m_2 = \frac{1}{3}$

Lastly, we calculate the equation of the line using:

$y - y_1 = m_2(x - x_1)$

The line segment has a midpoint at (3, 1)

So:

$y - 1 = \frac{1}{3}(x - 3)$

Open bracket

$y - 1 = \frac{1}{3}x - 1$

Add 1 to both sides

$y - 1 +1= \frac{1}{3}x - 1+1$

$y = \frac{1}{3}x$

Hence, the equation of the line segment is: $y = \frac{1}{3}x$

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A garage door that is 16 feet wide and 7 feet high is being painted the door have three windows that will not be painted each re

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