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The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is?
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The length of the perpendicular from the point (2,5) on the line 4x-3y...
Finding the Length of the Perpendicular from the Point (2,5) on the Line 4x-3y=18
To find the length of the perpendicular from a point to a line, we need to follow these steps:
Step 1: Find the equation of the line
The equation of the line can be written in the slope-intercept form y=mx+b, where m is the slope of the line and b is the y-intercept. However, the given equation 4x-3y=18 is not in the slope-intercept form. So, we need to convert it into that form.
4x-3y=18
-3y=-4x+18
y=(4/3)x-6
Therefore, the equation of the line is y=(4/3)x-6.
Step 2: Find the slope of the line
The slope of the line is the coefficient of x in the equation of the line. So, the slope of the line y=(4/3)x-6 is 4/3.
Step 3: Find the slope of the perpendicular line
The slope of the perpendicular line is the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is -3/4.
Step 4: Find the equation of the perpendicular line
We can use the point-slope form of a line to find the equation of the perpendicular line. The point-slope form of a line is y-y1=m(x-x1), where m is the slope of the line and (x1,y1) is a point on the line. In this case, we can use the point (2,5) on the perpendicular line and the slope -3/4 to get the equation of the perpendicular line.
y-5=(-3/4)(x-2)
y=(-3/4)x+(23/4)
Therefore, the equation of the perpendicular line is y=(-3/4)x+(23/4).
Step 5: Find the point of intersection of the two lines
The point of intersection of the two lines is the point where the perpendicular line passes through the given line. To find this point, we need to solve the system of equations:
y=(4/3)x-6
y=(-3/4)x+(23/4)
Solving the system of equations, we get x=6 and y=-2.
Therefore, the point of intersection of the two lines is (6,-2).
Step 6: Find the distance between the point and the line
The distance between the point (2,5) and the line 4x-3y=18 is the distance between the point and the point of intersection of the two lines. We can use the distance formula to find this distance
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The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is?
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The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is?.
The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the perpendicular from the point (2,5) on the line 4x-3y 18 0 is?.
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