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Alenkinab [10]
3 years ago
14

Given points A (1, 2/3), B (x, -4/5), and C (-1/2, 4) determine the value of x such that all three points are collinear

Mathematics
1 answer:
AlladinOne [14]3 years ago
8 0

Answer:

x=\frac{83}{50}

Step-by-step explanation:

we know that

If the three points are collinear

then

m_A_B=m_A_C

we have

A (1, 2/3), B (x, -4/5), and C (-1/2, 4)

The formula to calculate the slope between two points is equal to

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

step 1

Find the slope AB

we have

A(1,\frac{2}{3}),B(x,-\frac{4}{5})

substitute in the formula

m_A_B=\frac{-\frac{4}{5}-\frac{2}{3}}{x-1}

m_A_B=\frac{\frac{-12-10}{15}}{x-1}

m_A_B=-\frac{22}{15(x-1)}

step 2

Find the slope AC

we have

A(1,\frac{2}{3}),C(-\frac{1}{2},4)

substitute in the formula

m_A_C=\frac{4-\frac{2}{3}}{-\frac{1}{2}-1}

m_A_C=\frac{\frac{10}{3}}{-\frac{3}{2}}

m_A_C=-\frac{20}{9}

step 3

Equate the slopes

m_A_B=m_A_C

-\frac{22}{15(x-1)}=-\frac{20}{9}

solve for x

15(x-1)20=22(9)

300x-300=198

300x=198+300

300x=498

x=\frac{498}{300}

simplify

x=\frac{83}{50}

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<u><em>Answer:</em></u>

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<u>The general form of the equation of a line in point-slope form is:</u>

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<u>where:</u>

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<u>The general form of the equation of a line in slope-intercept form is:</u>

y = mx + c

<u>where:</u>

m is the slope

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<u>1- Getting the point:</u>

We are already given the point (-3 , -2) so we'll directly use it

<u>2- Getting the slope</u>

<u>We are given that our line is parallel to the line:</u>

y = 1x - 7

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<u>This means that:</u>

slope of the line we want = 1

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Answer:

Step-by-step explanation:

4) d = 12 cm; r = 12/2 = 6cm ; h = 5 cm

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5) d = 8 cm ; r = 8/2 = 4cm ; h = 7cm

S.A = 2πr(r + h)

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         = 60 + 40 + 96 + 104

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