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3 years ago

12

When you use the distance formula, you are calculating the length of the (fill in blank) of a right triangle

2 answers:

Lera25 [3.4K]3 years ago

7 0

Answer:

We are calculating the Hypotenuse of a right triangle.

Step-by-step explanation:

<u> Distance Formula:</u> When working on a coordinate plane, you can always find the distance between two points (or the length of a line segment) by creating a right triangle and using the Pythagorean Theorem. Draw a right triangle such that the distance between the two points is the <em>hypotenuse.</em>

Hence, When you use the distance formula, you are calculating the length of the<u> Hypotenuse</u> of a right triangle.

We could also see from the figure attached.

melamori03 [73]3 years ago

4 0

Generally, if you have to use the distance formula, you are finding the hypotenuse.

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Perpendicular to the line 4x - 6y + 7 = 0 , passing through (3, 4) .

PilotLPTM [1.2K]

Answer:

The equation of line perpendicular to given line passing through (3,4) is:

$y = -\frac{3}{2}x+\frac{17}{2}$

Step-by-step explanation:

Given equation of line is:

$4x - 6y + 7 = 0$

Given equation is in standard form. It has to be converted into slope-intercept form to extract slope from the equation.

So,

$4x+7 = 6y\\6y=4x+7\\\frac{6y}{6} = \frac{4x+7}{6}\\y = \frac{4}{6}x+\frac{7}{6}\\y=\frac{2}{3}x+\frac{7}{6}$

The standard form of slope-intercept form of equation is:

$y=mx+b$

Here, the co-efficient of x is the slope of the line.

So the slope of given line is: 2/3

m = 2/3

The product of slopes of two perpendicular lines is -1

Let m1 be the slope of line perpendicular to given line

Then

$m.m_1 = -1\\\frac{2}{3} . m_1 = -1\\m_1 = -1*\frac{3}{2}\\m_1 = -\frac{3}{2}$

The equation of perpendicular will be:

$y = m_1x+b$

Putting the value of slope

$y = -\frac{3}{2}x+b$

To find the value of b, putting (3,4) in the equation

$4 = -\frac{3}{2}(3)+b\\4 = -\frac{9}{2}+b\\b = 4+\frac{9}{2}\\b= \frac{8+9}{2}\\b=\frac{17}{2}$

So the equation of line perpendicular to given line passing through (3,4) is:

$y = -\frac{3}{2}x+\frac{17}{2}$

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shtirl [24]

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(3x-14)+x=90
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4x=104
x=26

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