find an equation of the line containing, (4,-2) and parallel to the line containing (-1,4) and (2,-3)
find an equation of the line containing (-1, 3) and perpendicular to the line containing (3,-5) and (-2,7)
You have to find the slope of the other line.
On the second: slope= changey/changeX
= -5-7 / 3+2=-12/5
On the second, perpendicular means the new line has a slope of 5/12.
To find the equation of a line parallel or perpendicular to another line, we need to know the slope of the given line.
Let's start with the first question:
1. Find the slope of the line containing (-1,4) and (2,-3).
We can use the formula for slope: slope = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we get: slope = (-3 - 4) / (2 - (-1)) = -7/3
So, the slope of the line is -7/3.
2. Since we want to find a line parallel to this line, the slope of the new line will also be -7/3.
3. We have the point (4,-2) on the line we want to find. We can now use the point-slope form of the equation of a line.
The equation is: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Plugging in the values, we get: y - (-2) = (-7/3)(x - 4)
Simplifying, we get: y + 2 = (-7/3)x + 28/3
Rearranging the equation to the standard form, we get: 7x + 3y = 22
So, the equation of the line containing (4,-2) and parallel to the line containing (-1,4) and (2,-3) is 7x + 3y = 22.
Now, let's move on to the second question:
1. Find the slope of the line containing (3,-5) and (-2,7).
Using the slope formula again, we have: slope = (7 - (-5)) / (-2 - 3) = 12/(-5) = -12/5
Hence, the slope of the line is -12/5.
2. We want to find a line perpendicular to this line. The slope of the perpendicular line is the negative reciprocal of -12/5.
The negative reciprocal of a/b is -b/a. So, the slope of the perpendicular line is 5/12.
3. We have the point (-1,3) on the line we want to find. We can now use the point-slope form of the equation.
Plugging in the values, we get: y - 3 = (5/12)(x - (-1))
Simplifying, we get: y - 3 = (5/12)(x + 1)
Rearranging the equation to the standard form, we get: 5x - 12y = -27
So, the equation of the line containing (-1, 3) and perpendicular to the line containing (3,-5) and (-2,7) is 5x - 12y = -27.