Revision (Grade 12 NSC Matric Mathematics): Flashcards

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Distance formula for points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)

(x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Gradient formula

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Midpoint formula

M=(x1+x22,y1+y22)M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Gradient-intercept form of line

y=mx+cy = mx + c

Equation of horizontal line

y=ky = k (constant)

Equation of vertical line

x=kx = k (constant)

Relationship between gradient mm and inclination θ\theta

m=tan⁡θm = \tan \theta for 0°≤θ<180°0° \leq \theta < 180°

Condition for parallel lines

m1=m2m_1 = m_2

Condition for perpendicular lines

m1×m2=−1m_1 \times m_2 = -1

Finding inclination with negative gradient

Add 180° to reference angle

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