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astraxan [27]
1 year ago
10

Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −3x+5y=−15? Drag and drop each choice in

to the boxes to correctly complete the table.
Mathematics
1 answer:
nexus9112 [7]1 year ago
5 0

The first line is perpendicular, the second line is not perpendicular and not parallel , the third line is parallel to the above line and the forth line not parallel or perpendicular to the line.

<h3>How can the slope of the line be calculate?</h3>

The slope of the line  is been given as −3x+5y=−15

Then y= \frac{3}{5x} -3, hence the slope is \frac{3}{5}

  • Slope of the first line 5x + 3y = 15 after calculation is

the slope is y= \frac{5}{-3x} +5\\\\\frac{5}{-3}

this means that the line is perpendicular to the given line

  • Slope of the second line  3x + 5y = 15 after calculation is

y= \frac{3}{-5x} +15\\\\\frac{3}{-5}

This means that the line is not perpendicular and not parallel

  • Slope of the Third line  -3x + 5y = 15 can be calculated as

y= \frac{3}{5x} +15\\\\\frac{3}{5}

This means that the line is parallel to the above line.

  • Slope of the first line  3x + 5y = 15 after calculation is

y= \frac{-3}{5x} +3\\\\\frac{-3}{5}

This means that the line is not parallel or perpendicular to the line

Learn more about slope of  line at:

brainly.com/question/3493733

#SPJ1

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Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W
Serhud [2]

The coordinates of the vertex W are (5 , -1)

Step-by-step explanation:

In the parallelogram, the diagonal bisect each other

To find a missing vertex in a parallelogram do that:

  • Find the mid-point of a diagonal whose endpoints are given
  • Use this mid-point to find the missing vertex
  • The mid point rule is (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

∵ WXYZ is a parallelogram

∴ Its diagonals are WY and XZ

∵ The diagonal bisect each other

- That mean they have the same mid-point

∴ They intersect each other at their mid-point

∵ x = (-2 , -3) and z = (7 , 7)

∴ x_{1} = -2 and x_{2} = 7

∴ y_{1} = -3 and y_{2} = 7

- Substitute them in the rule of the mid point to find the

   mid-point of XZ

∴ M_{XZ}=(\frac{-2+7}{2},\frac{-3+7}{2})=(2.5 , 2)

∴ The mid-point of diagonals WY and XZ is (2.5 , 2)

Let us use it to find the coordinates of vertex W

∵ W = (x , y) and Y = (0 , 5)

∴ x_{1} = x and x_{2} = 0

∴ y_{1} = y and y_{2} = 5

- Equate 2.5 by the rule of the x-coordinate of the mid-point

∵ 2.5=\frac{x+0}{2}

- Multiply both sides by 2

∴ 5 = x + 0

∴ 5 = x

∴ The x-coordinate of point W is 5

- Equate 2 by the rule of the y-coordinate of the mid-point

∵ 2=\frac{y+5}{2}

- Multiply both sides by 2

∴ 4 = y + 5

- Subtract 5 from both sides

∴ -1 = y

∴ The y-coordinate of point W is -1

The coordinates of the vertex W are (5 , -1)

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

#LearnwithBrainly

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