Triangle with One Point at (0,0) (Leaving Cert Mathematics): Flashcards

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Triangle with One Point at (0,0)
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Area formula for triangle at (0,0)(0,0), (x1,y1)(x_1,y_1), (x2,y2)(x_2,y_2)

12∣x1y2−x2y1∣\frac{1}{2}|x_1y_2 - x_2y_1|

Length from (0,0)(0,0) to (x1,y1)(x_1,y_1)

x12+y12\sqrt{x_1^2 + y_1^2}

Length from (0,0)(0,0) to (x2,y2)(x_2,y_2)

x22+y22\sqrt{x_2^2 + y_2^2}

Length from (x1,y1)(x_1,y_1) to (x2,y2)(x_2,y_2)

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

Slope from (0,0)(0,0) to (x1,y1)(x_1,y_1)

m=y1x1m = \frac{y_1}{x_1}

Line equation from origin through (x1,y1)(x_1,y_1)

y=mxy = mx where m=y1x1m = \frac{y_1}{x_1}

Slope from (x1,y1)(x_1,y_1) to (x2,y2)(x_2,y_2)

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

Point-slope eq. from (x1,y1)(x_1,y_1) to (x2,y2)(x_2,y_2)

y−y1=m(x−x1)y - y_1 = m(x - x_1)

What does vertex at origin simplify?

Area, side lengths, slopes & equations of sides

Area of triangle (0,0)(0,0), (3,4)(3,4), (6,2)(6,2)

99 square units

Length from (0,0)(0,0) to (3,4)(3,4)

55 units

Key benefit of triangle with vertex at (0,0)(0,0)

Simplifies coordinate geometry calculations

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