Determine the equation of the lines perpendicular to the given lines and passing through the given points:(a)(1,4) and (-1,1) (b) (3,3) and (-1,-1)
a. 4-1/-2-1 = 3-1/3-1
b. 4-1/-2-1 = 3-(-1)/3-1
c. 4-1/1-(-2)= 3-(-1)/3-(-1)
d. 1-(-2)/4-1 = 3-1/3-1
Are those supposed to be your answers ?
None make any sense, since it asked for the equation of the line
I will do a)
2 points (1,4) and -1,1)
slope = (1-4)/(-1-1) = -3/-2 = 3/2 , note that the brackets in the first calculation are essential
using the point (1,4)
y-4 = (3/2)(x-1)
times 2, the LCD
2y - 8 = 3(x-1)
2y - 8 = 3x- 3
3x - 2y = -5 OR 3x-2y+5=0 OR y= (3/2)x + 5/2
try b) the same way
Thank you. Those are the choices I have to pick
I should have read your question a bit more carefully
It asked for the equation of the lines perpendicular to the line joining the points
Now the question makes even less sense, since we don't know through which point our perpendicular will pass
Your answers appear to find slope, but without brackets nothing makes sense
sorry I wrote problem wrong:
Which equation would you use to find out if the two lines in the graph are parallel:(a)(1,4) and (-1,1) (b) (3,3) and (-1,-1)
a. 4-1/-2-1 = 3-1/3-1
b. 4-1/-2-1 = 3-(-1)/3-1
c. 4-1/1-(-2)= 3-(-1)/3-(-1)
d. 1-(-2)/4-1 = 3-1/3-1
To determine the equation of a line that is perpendicular to a given line and passes through a given point, you need to follow these steps:
Step 1: Find the slope of the given line
You can find the slope of a line using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Calculate the slope of the given line using the given points.
For case (a):
slope = (1 - 4) / (-1 - 1)
slope = -3 / -2
slope = 3/2
For case (b):
slope = (-1 - 3) / (-1 - 3)
slope = -4 / -4
slope = 1
Step 2: Find the negative reciprocal of the slope
The negative reciprocal of a number is obtained by flipping its sign and taking the reciprocal. In other words, if the slope is m, then the negative reciprocal is -1/m.
For case (a):
negative reciprocal = -1 / (3/2)
negative reciprocal = -2/3
For case (b):
negative reciprocal = -1 / 1
negative reciprocal = -1
Step 3: Use the negative reciprocal slope and the given point to find the equation of the perpendicular line
Now that you have the negative reciprocal slope, you can use the given point and the point-slope form of a line to find the equation of the perpendicular line. The point-slope form is: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the negative reciprocal slope.
For case (a):
Using the point (1, 4), the equation of the perpendicular line is:
y - 4 = (-2/3)(x - 1)
For case (b):
Using the point (3, 3), the equation of the perpendicular line is:
y - 3 = (-1)(x - 3)
So, the equations of the lines perpendicular to the given lines and passing through the given points are:
(a) y - 4 = (-2/3)(x - 1)
(b) y - 3 = (-1)(x - 3)