IB Mathematics SL – Straight Lines

IB Mathematics SL, Coordinate geometry, Straight Lines

1. IB Mathematics SL, Coordinate geometry, Distance between two points

How can we find the distance between two points B(1,6) and C(-4,7) ?

Solution

IB Math SL, Coordinate geometry, Distance Formula The distance between two points B(x_{1}, y_{1}) and C(x_{2}, y_{2}) is given by the following formula: d_{BC}= \sqrt{( x_{2}- x_{1})^2+( y_{2}- y_{1})^2} Applying the distance formula in our case we have d_{BC}= \sqrt{( -4- 1)^2+( 7-6)^2}=\sqrt{25+1}=\sqrt{26}

2. IB Mathematics SL, Coordinate geometry, Gradient of a line

How can we find the slope of the line passes through these points B(4,7) and C(3,8)?

Solution

IB Math SL, Coordinate geometry, Gradient of a line The gradient m of the line passes through two points B(x_{1}, y_{1}) and C(x_{2}, y_{2}) is given by the following formula: m=\frac{ y_{2}- y_{1}}{ x_{2}- x_{1}} Applying the above formula in our case we have m=\frac{8-7}{3-4}=\frac{1}{-1}=-1

3. IB Mathematics SL, Slope of a line, perpendicular & parallel lines

How can we find the slope of the line which is perpendicular to the line y=4x+7 ?

Solution

IB Math SL, gradient of a line, perpendicular – parallel lines If two lines are perpendicular their slopes are negative reciprocals and if two lines are parallel have equal slopes. Regarding your question about the gradient of the line which is perpendicular to the line y=4x+7, Let m be the required slope then we have the following relation m \cdot 4=-1 =>m=\frac{-1}{4}=- \frac{1}{4}

4. IB Mathematics SL, midpoint formula

How can we find the coordinates of the midpoint of line segment BC where B(2,6) and C(-1,-8) ?

Solution

IB Math SL, midpoint formula. The coordinates of the midpoint of a line segment defined by the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is given by the following formula: (x_{m}, y_{m} )=( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} ) Applying the above formula in our case we have (x_{m}, y_{m} )=( \frac{2-1}{2},\frac{6-8}{2} )= =( \frac{1}{2},\frac{-2}{2} ) =( \frac{1}{2},-1)

Find the Equation of a Line in Slope Intercept Form Given Two Points