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प्रश्न
The line through A(–2, 3) and B(4, b) is perpendicular to the line 2x – 4y = 5. Find the value of b.
उत्तर
Slope of the line through A(–2, 3) and B(4, b) = `m_1 = (y_2 - y_1)/(x_2 - x_1) = (b - 3)/(4+2) = (b -3)/6`
Equation of given line is 2x - 4y - 5 = 0
`=> 4y = 2x - 5`
`=> y = 1/2 x - 5/4`
∴ Slope of given line = `m_2 = 1/2`
Since the lines are perpendicular therefore `m_1 xx m_2 = -1`
`=> (b - 3)/6 xx 1/2 = -1`
`=> b -3 = -12 => b = -9`
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संबंधित प्रश्न
Find the slope of the line with inclination 30° .
Find the slope of the line passing through the points A(-2, 1) and B(0, 3).
Without using the distance formula, show that the points A(4, −2), B(−4, 4) and C(10, 6) are the vertices of a right-angled triangle.
The line through A(−2, 3) and B(4, b) is perpendicular to the line 2x – 4y = 5. Find the value of b.
Find the slope of a line, correct of two decimals, whose inclination is 50°
Find the slope of a line passing through the given pair of points (9,-2) and (-5,5)
Find the slope of a line parallel to the given line 5x + 2y = 11
Given that (a, 2a) lies on line`(y)/(2) = 3 - 6`.Find the value of a.
Determine whether the following points are collinear. A(–1, –1), B(0, 1), C(1, 3)
Given: Points A(–1, –1), B(0, 1) and C(1, 3)
Slope of line AB = `(square - square)/(square - square) = square/square` = 2
Slope of line BC = `(square - square)/(square - square) = square/square` = 2
Slope of line AB = Slope of line BC and B is the common point.
∴ Points A, B and C are collinear.
