Maths 1 week 2 Summary

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Coordinate Geometry Formulas

Distance Formula Between Two Points

Explanation: Calculates the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$.

Formula: $d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Section Formula

Explanation: Determines the coordinates of a point dividing a line segment internally in the ratio $m:n$.

Formula: $(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Area of Triangle When Three Coordinates Given

Explanation: Calculates the area of a triangle with vertices at $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$.

Formula: $\text{Area}=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

Parallel Lines

Explanation: Lines with the same slope.

Formula: If $m_1=m_2$, the lines are parallel.

Perpendicular Lines

Explanation: Lines with slopes that are negative reciprocals.

Formula: If $m_1\cdot m_2=-1$, the lines are perpendicular.

Slope of a Line

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Relation of Slope of Two Perpendicular and Parallel Lines

Explanation: Parallel lines have equal slopes; perpendicular lines have slopes that multiply to $-1$.

Formula: Parallel: $m_1=m_2$, Perpendicular: $m_1\cdot m_2=-1$

Representation of Line

Explanation: General form of a line equation.

General equation: $Ax+By+C=0$

Slope-intercept form: $y=mx+c$

Point slope form: $y-y_0=m(x-x_0)$

Two point form: $y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$

Slope intercept form: $\frac{x}{a}+\frac{y}{b}=1$

Equation of Two Perpendicular and Parallel Lines

Explanation: Equations for lines based on their slopes.

Formula: Parallel: $y=mx+c$, Perpendicular: $y=-\frac{1}{m}x+c$

Equation of Perpendicular Line Passing Through a Point

Explanation: Finds the equation of a line perpendicular to a given line passing through a specific point $(x_1,y_1)$.

Formula: $y-y_1=-\frac{1}{m}(x-x_1)$

Distance of a Line from a Given Point

Explanation: Calculates the perpendicular distance from a point $(x_1,y_1)$ to a line $Ax+By+C=0$.

Formula: $d=\frac{|A{x}_1+B{y}_1+C|}{\sqrt{A^2+B^2}}$

Angle Between Two Lines

If two lines have slopes m1 and m2, the angle theta between them is given by:

$$\tan \theta =\left|\frac{m_2-m_1}{1+m_1{m}_2}\right|$$

Sum Squared Error

Explanation: Measures the total deviation of predicted values from actual values.

Formula: $SSE=\sum _{i=1}^n(y_i-{\hat{y}}_i{)}^2$

Week 2 summary video

Notes and activity question

Graded assignment