What are the equations of lines m and q?

The equation of line m is:

  Equation of 'm'

   (y - 6) = - ³/₅ (x - 2)     [point-slope form]

           y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

    Equation of 'q'

     (y - 6) = ⁵/₃ (x - 2)         [point-slope form]

            y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

Step-by-step explanation:

To find the equation for both 'm' and 'q' requires a bit of work. Because neither  'm' nor 'q' has two points to find the slopes of the line, we have to get creative.

Line 'n' has two points [ (4, 4) & (1, -1) ], and as such we can find the slope of that line.  Luckily for us, line 'n' is parallel with 'q' and perpendicular with m.

Finding the slope of 'n'

The slope of the 'n'    =  (y₂ - y₁) ÷ (x₂ - x₁)      

                                    =  (4 - (- 1)) ÷ (4 - 1)  

                                    =  5 ÷ 3

                                    =  ⁵/₃

Determine the slope of 'q' and 'm'

            Since 'n' and 'q' are parallel,

                           then the slope of q = ⁵/₃

             Since 'n' and 'm' are perpendicular

                           then the slope of m = - ³/₅

Write the equation for 'q' and 'm'

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for the lines

For both 'q' and 'm' let (x₁, y₁) be (2, 6)

    Equation of 'm'

   (y - 6) = - ³/₅ (x - 2)     [point-slope form]

           y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

    Equation of 'q'

     (y - 6) = ⁵/₃ (x - 2)         [point-slope form]

            y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.