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Ex 9.1, 2 - Chapter 9 Class 11 Straight Lines
Last updated at April 16, 2024 by Teachoo
Cordinate geometry questions
Chapter 9 Class 11 Straight Lines
Concept wise
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Cordinate geometry questions
- Slope - Finding slope
- Slope - Prependicularity
- Angle between two lines by Slope
- Collinearity of 3 points by sliope
- Point Slope form
- Slope-Intercept form
- Intercept form
- Normal form
- Given Statement
- Two lines // or/and prependicular
- Angle between two lines
- Distance - Between two parallel lines
- Distance of a point from a line
- Distance of a point from a line along a line
- Other Type of questions - Area of Triangle formed
- Other Type of questions - 3 lines Concurrent
- Other Type of questions - Image
- Other Type of questions - Mix
Transcript
Ex10.1, 2 The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle. Let ABC be an equilateral triangle In equilateral triangle all sides are equal So, AB = BC = AC = 2a Given that the base of equilateral triangle i.e. BC lies along the y-axis such that mid point of BC is O(0, 0) So, OB = OC = a Coordinates of C = (a, 0) & Coordinates of B = ( a, 0) Also, Since O is the mid-point of BC OA is the median of ABC In equilateral triangle, median & altitude is same. So, OA is the altitude of ABC If OA is the altitude of ABC, then OA is perpendicular to BC So, point A lies on y-axis as y-axis is perpendicular to x-axis Since point A lie on the y-axis its x coordinate will be 0 So, Coordinates of point A = (0, y) Now, AB = 2a Distance between (0, y) & ( a, 0) is 2a (( 2 1)2 + ( 2 1)2) = 2a (( 0)2 + (0 )2) = 2a (( )2 + ( )2) = 2a ( ^2+ ^2 ) = 2a Squaring both sides ( ( ^2+ ^2 ))^2 = (2a)2 a2 + y2 = 4a2 y2 = 4a2 a2 y2 = 3a2 y = (3 ^2 ) y = a 3 So, Point A = (0, y) A = (0, a 3) and (0, a 3) Hence vertices of triangle ( 3, 0)(0, -a)(o, -a)& (-a 3, 0)(0, a)&(0, -a) So, Point A = (0, y) A = (0, a 3) and (0, a 3) Hence vertices of triangle ( a, 0) , (a, 0) , (0, a 3) and ( a, 0) , (a, 0), (0, a 3)
