perpendicular - two lines which intersect to form a right angle
2 Lines Intersection
Free 2 Lines Intersection Calculator - Enter any 2 line equations, and the calculator will determine the following:
* Are the lines parallel?
* Are the lines perpendicular
* Do the lines intersect at some point, and if so, which point?
* Is the system of equations dependent, independent, or inconsistent
Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to
Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3).
Step 1: Find the slope of the line 4x + y = 8.
In y = mx + b form, we have y = -4x + 8.
The slope is -4.
To be perpendicular to a line, the slope must be a negative reciprocal of the line it intersects with.
Reciprocal of -4 = -1/4
Negative of this = -1(-1/4) = 1/4
Using our [URL=' calculator[/URL], we get [B]y = 1/4x + 2[/B]
Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and
Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept
Get this in slope-intercept form by adding 5y to each side:
4x - 5y + 5y = 5y + 20
Cancel the 5y's on the left side and we get:
5y + 20 = 4x
Subtract 20 from each side
5y + 20 - 20 = 4x - 20
Cancel the 20's on the left side and we get:
5y = 4x - 20
Divide each side by 5:
5y/5 = 4x/5 - 4
y = 4x/5 - 4
So we have a slope of 4/5
to find our y-intercept, we set x = 0:
y = 4(0)/5 - 4
y = 0 - 4
y = -4
If we want a line perpendicular to the line above, our slope will be the negative reciprocal:
The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator:
m = 5/4
Next, we multiply this by -1:
-5/4
So our slope-intercept of the perpendicular line with the same y-intercept is:
[B]y = -5x/4 - 4[/B]
If MN is perpendicular to PQ and the slope of PQ is -4 what is the slope for MN
If MN is perpendicular to PQ and the slope of PQ is -4 what is the slope for MN
the slope of a line perpendicular to another line is the negative reciprocal. Therefore:
Slope of MN = -1/Slope of PQ
Slope of MN = -1/-4
Slope of MN = [B]1/4[/B]
If the slope is 6 what would the slope of a line parallel to it be?
If the slope is 6 what would the slope of a line parallel to it be?
Our rule for the relation of second lines to first lines with regards to slope is this:
[LIST]
[*]Parallel lines have the [U]same[/U] slope
[*]Perpendicular lines have the [U]negative reciprocal[/U] slope
[/LIST]
So the slope of the line parallel would also be [B]6[/B]
Line m passes through points (3, 16) and (8, 10). Line n is perpendicular to m. What is the slope of
Line m passes through points (3, 16) and (8, 10). Line n is perpendicular to m. What is the slope of line n?
First, find the slope of the line m passing through points (3, 16) and (8, 10).
[URL=' the points into our search engine[/URL], we get a slope of:
m = -6/5
If line n is perpendicular to m, then the slope of n is denote as:
n = -1/m
n = -1/-6/5
n = -1*-5/6
n = [B]5/6[/B]
Line m passes through points (7, 5) and (9, 10). Line n passes through points (3, 1) and (7, 10). Ar
Line m passes through points (7, 5) and (9, 10). Line n passes through points (3, 1) and (7, 10). Are line m and line n parallel or perpendicular
[U]Slope of line m is:[/U]
(y2 - y1)/(x2 - x1)
(10 - 5)/(9 - 7)
5/2
[U]Slope of line n is:[/U]
(y2 - y1)/(x2 - x1)
(10 - 1)/(7 - 3)
9/4
Run 3 checks on the slopes:
[LIST=1]
[*]Lines that are parallel have equal slopes. Since 5/2 does not equal 9/4, these lines [B]are not parallel[/B]
[*]Lines that are perpendicular have negative reciprocal slopes. Since 9/4 is not equal to -2/5 (the reciprocal of the slope of m), these lines [B]are not perpendicular[/B]
[*][B]Therefore, since the lines are not parallel and not perpendicular[/B]
[/LIST]
Plane and Parametric Equations in R3
1) Plane Equation passing through (x,y,z) perpendicular to A
2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A
The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete
The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000.
[LIST]
[*]h = b + 70
[*]A = 1/2bh = 3000
[/LIST]
Substitute the height equation into the area equation
1/2b(b + 70) = 3000
Multiply each side by 2
b^2 + 70b = 6000
Subtract 6000 from each side:
b^2 + 70b - 6000 = 0
Using our [URL=' calculator[/URL], we get:
b = 50 and b = -120
Since the base cannot be negative, we use b = 50.
If b = 50, then h = 50 + 70 = 120
The perimeter is b + h + hypotenuse
Using the [URL=' calculator[/URL], we get hypotenuse = 86.02
Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]
Vectors
Free Vectors Calculator - Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.
What is a Perpendicular Bisector
Free What is a Perpendicular Bisector Calculator - This lesson walks you through what a perpendicular bisector is and the various properties of the segment it bisects and the angles formed by the bisection
