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17 Aug 2020, 19:35
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Line A, of which equation is ax+by=c, is perpendicular to line M passing through (2c,0). What is the equation of line M in terms of a, b and c?
17 Aug 2020, 21:43
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When 2 lines are perpendicular the slopes of the 2 lines are related as \(m_1\) * \(m_2\) = -1, where m1 is the slope of line 1 and m2 is the slope of line 2.
Let us take line 1 first which is given as ax + by = c here a and b are coefficients of a and b respectively and c is a constant.
We convert this into a y = mx + b form, where m is the slope and b is called the y intercept.
We do this by isolating y on the left hand side.
by =-ax + c
So y = -\(\frac{a}{b}\) x + \(\frac{c}{b}\)
Slope of line 1 i.e \(m_1\) = -\(\frac{a}{b}\)
We know that for perpendicular lines \(m_1\) * \(m_2\) = -1
-\(\frac{a}{b}\) * \(m_2\) = -1
\(m_2\) = \(\frac{b}{a}\)
We now use the slope intercept form \(y - y_1\) = \(m (x - x_1\)), to find the equation of the second line.
m = \(m_2\) = \(\frac{b}{a}\) and (\(x_1\), \(y_1\)) = (2c, 0)
Substituting we get y - 0 = \(\frac{b}{a}\) (x - 2c)
or y = \(\frac{b}{a}\) (x - 2c)
Arun Kumar
Some important Key Points
(1) The intercept is the point where the line cuts the x axis (x intercept) and the y axis (the y intercept)
(2) For lines that that are perpendicular, the relationship between slopes is \(m_1\) * \(m_2\) = -1.
For parallel lines \(m_1\) = \(m_2\)
(3) There are 4 methods of creating the equation of the line based on given data
(i) Slope Intercept Method:
When the slope, m and the y intercept b is given, then equation of the line is y = mx + b
(ii) Slope Point Method:
When the slope, m and a point (\(x_1\), \(y_1\)), through which the line passes is given, then equation of the line is \(y - y_1\) = \(m (x - x_1)\)
(iii) Double Point Method:
When it is given that the line passes through 2 points (\(x_1\), \(y_1\)) and (\(x_2\), \(y_2\)), then first find the slope using
\(\frac{y_2 - y_1}{x_2 - x_1}\) = and then use the slope point form for any of the points
\(y - y_1\) = \(m (x - x_1)\) or \(y - y_2\) = \(m (x - x_2)\)
(iv) Double Intercept Method:
When the x intercept = a and y intercept = b are given, then the equation of the line is
\(\frac{x}{a} + \frac{y}{b} = 1 \)
Let us take line 1 first which is given as ax + by = c here a and b are coefficients of a and b respectively and c is a constant.
We convert this into a y = mx + b form, where m is the slope and b is called the y intercept.
We do this by isolating y on the left hand side.
by =-ax + c
So y = -\(\frac{a}{b}\) x + \(\frac{c}{b}\)
Slope of line 1 i.e \(m_1\) = -\(\frac{a}{b}\)
We know that for perpendicular lines \(m_1\) * \(m_2\) = -1
-\(\frac{a}{b}\) * \(m_2\) = -1
\(m_2\) = \(\frac{b}{a}\)
We now use the slope intercept form \(y - y_1\) = \(m (x - x_1\)), to find the equation of the second line.
m = \(m_2\) = \(\frac{b}{a}\) and (\(x_1\), \(y_1\)) = (2c, 0)
Substituting we get y - 0 = \(\frac{b}{a}\) (x - 2c)
or y = \(\frac{b}{a}\) (x - 2c)
Arun Kumar
Some important Key Points
(1) The intercept is the point where the line cuts the x axis (x intercept) and the y axis (the y intercept)
(2) For lines that that are perpendicular, the relationship between slopes is \(m_1\) * \(m_2\) = -1.
For parallel lines \(m_1\) = \(m_2\)
(3) There are 4 methods of creating the equation of the line based on given data
(i) Slope Intercept Method:
When the slope, m and the y intercept b is given, then equation of the line is y = mx + b
(ii) Slope Point Method:
When the slope, m and a point (\(x_1\), \(y_1\)), through which the line passes is given, then equation of the line is \(y - y_1\) = \(m (x - x_1)\)
(iii) Double Point Method:
When it is given that the line passes through 2 points (\(x_1\), \(y_1\)) and (\(x_2\), \(y_2\)), then first find the slope using
\(\frac{y_2 - y_1}{x_2 - x_1}\) = and then use the slope point form for any of the points
\(y - y_1\) = \(m (x - x_1)\) or \(y - y_2\) = \(m (x - x_2)\)
(iv) Double Intercept Method:
When the x intercept = a and y intercept = b are given, then the equation of the line is
\(\frac{x}{a} + \frac{y}{b} = 1 \)
General Discussion
17 Aug 2020, 19:38
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The answer of this question is y=(b/a)(x-2c).
But I have no idea how to approach this question... can someone help me please???
Thank you in advance!
Posted from my mobile device
But I have no idea how to approach this question... can someone help me please???
Thank you in advance!
Posted from my mobile device
