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elena-14-01-66 [18.8K]
3 years ago
6

PLLLLEEEEEEAAASSSSSSSSEEEE

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
8 0

Given:

Line a passes through (2, 10) and (4, 13).

Line b passes through (4, 9) and (6, 12).

Line c passes through (2, 10) and (4, 9).

To find:

Which of the lines, if any are perpendicular.

Solution:

If a line passes through two points, then the slope of line is

m=\dfrac{y_2-y_1}{x_2-x_1}

Line a passes through (2, 10) and (4, 13).  So, slope of this line is

m_a=\dfrac{13-10}{4-2}=\dfrac{3}{2}

Line b passes through (4, 9) and (6, 12).  So, slope of this line is

m_b=\dfrac{12-9}{6-4}=\dfrac{3}{2}

Line c passes through (2, 10) and (4,9).  So, slope of this line is

m_c=\dfrac{9-10}{4-2}=\dfrac{-1}{2}

Product of slopes of to perpendicular lines is -1.

m_a\cdot m_b=\dfrac{3}{2}\times \dfrac{3}{2}=\dfrac{9}{4}\neq -1

m_b\cdot m_c=\dfrac{3}{2}\times \dfrac{-1}{2}=\dfrac{-3}{4}\neq -1

m_a\cdot m_c=\dfrac{3}{2}\times \dfrac{-1}{2}=\dfrac{-3}{4}\neq -1

Therefore, any of these lines are not perpendicular to each other.

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Geometry</u>

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  • Area of a Circle: A = πr²

Step-by-step explanation:

<u>Step 1: Define</u>

d = 30 m

<u>Step 2: Find Area</u>

  1. Substitute [D]:                    30 m = 2r
  2. Isolate <em>r</em>:                             15 m = r
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  5. Rearrange:                        A = 15²π
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