Perpendicular Lines 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 7 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- Answered
- Review
-
Question 1 of 7
1. Question
Find the equation of a line that passes through `(4,2)` and is perpendicular to `y=-1/2x+9`Hint
Help VideoCorrect
Keep Going!
Incorrect
Point Gradient Form: `y-``y_1``=``m``(x-``x_1``)`
- `m` is the gradient of the line
- `(x_1,y_1)` is a point that lies on the line
Remember
The gradients of perpendicular lines are negative reciprocals of each other.First, identify the gradient of the given equation.In gradient-intercept form `(y=``m``x+b)`, `m` is the gradient.`y` `=` `-1/2``x+9` `m_1` `=` `-1/2` Get the negative reciprocal of the `m_1` by flipping it upside down and changing the sign.`m_1` `=` `-1/2` `=` `-2` Flip the number upside down `m_2` `=` `2` Change the sign Use the Point Gradient Formula to find the equation.Point: `(x_1,y_1)=(4,2)`Gradient: `m_2=2``y-``y_1` `=` `m``(x-``x_1``)` Point Gradient Formula `y-``2` `=` `2``(x-``4``)` Substitute values `y-2` `=` `2x-8` `y-2` `+2` `=` `2x-8` `+2` Add `2` to both sides `y` `=` `2x-6` Simplify `y=2x-6` -
Question 2 of 7
2. Question
Check if the line `y=2x+5` is perpendicular to the line `x+2y-6=0`.Hint
Help VideoCorrect
Well Done!
Incorrect
Gradient Intercept Form: `y=``m``x+``b`
- `m` is the gradient of the line
- `b` is the y-intercept (where the line cuts the y-axis)
Remember
To prove the perpendicularity of two lines, the product of their gradients should be equal to `-1`First, solve for the gradient of each line using the gradient formulaLine 1`y` `=` `2``x+5` `m_1` `=` `2` Line 2`x+2y-6` `=` `0` `x+2y-6` `-x+6` `=` `0` `-x+6` Add `-x+6` to both sides `2y` `=` `-x+6` Simplify `2y``-:2` `=` `(-x+6)``-:2` Divide both sides by `2` `y` `=` `-1/2``x + 3` `m_2` `=` `-1/2` To prove that these two lines are perpendicular, check if the product of the two gradients is equal to `-1`.`m_1 times m_2` `=` `2 times-1/2` `=` `-1` Therefore, Line `1` and Line `2` are perpendicular.Perpendicular
-
Question 3 of 7
3. Question
>Find the equation of a line that passes through `(-8,5)` and is perpendicular to `y=-4x+2`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Remember
The slope of perpendicular lines are negative reciprocals of each other.First, identify the slope of the given equation.In slope intercept form `(y= color(tomato)(m)x+b)`, `color(tomato)(m)` is the slope.`y` `=` `color(tomato)(-4)x+2` `m_1` `=` `-4` Get the negative reciprocal of the `m_1` by flipping it upside down and changing the sign.`m_1` `=` `-4` `=` `-1/4` Flip the number upside down `m_2` `=` `1/4` Change the sign Use the point slope formula to find the equation.Point: `(x_1,y_1)=(-8,5)`Slope: `m_2=1/4``y- color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` Point Slope Formula `y- color(royalblue)(5)` `=` `color(tomato)(1/4)(x- color(royalblue)(-8))` Substitute values `y-5` `=` `1/4x+2` `y-5 color(crimson)(+5)` `=` `1/4x+2 color(crimson)(+5)` Add `5` to both sides `y` `=` `1/4x+7` Simplify `y=1/4x+7` -
Question 4 of 7
4. Question
>Find the equation of a line that passes through `(-8,10)` and is perpendicular to `y=4x+6`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Remember
The slope of perpendicular lines are negative reciprocals of each other.First, identify the slope of the given equation.In slope intercept form `(y= color(tomato)(m)x+b)`, `color(tomato)(m)` is the slope.`y` `=` `color(tomato)(4)x+6` `m_1` `=` `4` Get the negative reciprocal of the `m_1` by flipping it upside down and changing the sign.`m_1` `=` `4` `=` `1/4` Flip the number upside down `m_2` `=` `-1/4` Change the sign Use the point slope formula to find the equation.Point: `(x_1,y_1)=(-8,10)`Slope: `m_2=-1/4``y- color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` Point Slope Formula `y- color(royalblue)(10)` `=` `color(tomato)(-1/4)(x- color(royalblue)(-8))` Substitute values `y-10` `=` `-1/4x+2` `y-10 color(crimson)(+10)` `=` `-1/4x+2 color(crimson)(+10)` Add `10` to both sides `y` `=` `-1/4x+12` Simplify `y=-1/4x+12` -
Question 5 of 7
5. Question
>Find the equation of a line that passes through `(-3,5)` and is perpendicular to `y=5x+6`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Remember
The slope of perpendicular lines are negative reciprocals of each other.First, identify the slope of the given equation.In slope intercept form `(y= color(tomato)(m)x+b)`, `color(tomato)(m)` is the slope.`y` `=` `color(tomato)(5)x+6` `m_1` `=` `5` Get the negative reciprocal of the `m_1` by flipping it upside down and changing the sign.`m_1` `=` `5` `=` `1/5` Flip the number upside down `m_2` `=` `-1/5` Change the sign Use the point slope formula to find the equation.Point: `(x_1,y_1)=(-3,5)`Slope: `m_2=-1/5``y- color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` Point Slope Formula `y- color(royalblue)(5)` `=` `color(tomato)(-1/5)(x- color(royalblue)(-3))` Substitute values `y-5` `=` `-1/5x+3/5` `y-5 color(crimson)(+5)` `=` `-1/5x+3/5 color(crimson)(+5)` Add `5` to both sides `y` `=` `-1/5x+28/5` Simplify `y=-1/5x+28/5` -
Question 6 of 7
6. Question
>Find the equation of a line that passes through `(4,-1)` and is perpendicular to `y=4x+8`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Remember
The slope of perpendicular lines are negative reciprocals of each other.First, identify the slope of the given equation.In slope intercept form `(y= color(tomato)(m)x+b)`, `color(tomato)(m)` is the slope.`y` `=` `color(tomato)(4)x+8` `m_1` `=` `4` Get the negative reciprocal of the `m_1` by flipping it upside down and changing the sign.`m_1` `=` `4` `=` `1/4` Flip the number upside down `m_2` `=` `-1/4` Change the sign Use the point slope formula to find the equation.Point: `(x_1,y_1)=(4,-1)`Slope: `m_2=-1/4``y- color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` Point Slope Formula `y- color(royalblue)(-1)` `=` `color(tomato)(-1/4)(x- color(royalblue)(4))` Substitute values `y+1` `=` `-1/4x+1` `y+1 color(crimson)(-1)` `=` `-1/4x+1 color(crimson)(-1)` Subtract `1` to both sides `y` `=` `-1/4x` Simplify `y=-1/4x` -
Question 7 of 7
7. Question
>Find the equation of a line that passes through `(-1,-4)` and is perpendicular to `9x+3y=8`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Remember
The slope of perpendicular lines are negative reciprocals of each other.First, convert the equation into gradient-intercept form and identify the gradient.In gradient-intercept form `(y=``m``x+b)`, `m` is the gradient.`9x+3y` `=` `8` `9x+3y` `-9x` `=` `8` `-9x` Subtract `9x` on both sides `3y` `=` `8-9x` `3/3y` `=` `8/3-9/3x` Divide all terms by `3` `y` `=` `-3x+8/3` Then, identify the slope of the given equation.In slope intercept form `(y= color(tomato)(m)x+b)`, `color(tomato)(m)` is the slope.`y` `=` `color(tomato)(-3)x+8/3` `m_1` `=` `-3` Get the negative reciprocal of the `m_1` by flipping it upside down and changing the sign.`m_1` `=` `-3` `=` `-1/3` Flip the number upside down `m_2` `=` `1/3` Change the sign Use the point slope formula to find the equation.Point: `(x_1,y_1)=(-1,-4)`Slope: `m_2=1/3``y- color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` Point Slope Formula `y- color(royalblue)(-4)` `=` `color(tomato)(1/3)(x- color(royalblue)(-1))` Substitute values `y+4` `=` `1/3x+1/3` `y+4 color(crimson)(-4)` `=` `1/3x+1/3 color(crimson)(-4)` Subtract `4` to both sides `y` `=` `1/3x-11/3` Simplify `y=1/3x-11/3`