Mathematics: Prove that the line passing through points A (4.1) and B (-1.3) is perpendicular to the line passing through points G (4, -2) and D (6.3). Also find the equations AG, BD and the point of intersection of AB, GD

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Prove that the line passing through points A (4.1)

laykaleb086

17.01.2022

See below

Step-by-step explanation:

Find the slope of each line:

m(AB) = (3 - 1)/(- 1 - 4) = 2 / - 5 = - 2/5m(GD) = (3 + 2)/(6 - 4) = 5/2

The product of the slopes is - 1, hence the lines are perpendicular:

- 2/5 * 5/2 = - 1

Equation of each line

Line AB

y - 1 = -2/5(x - 4) ⇒ y = - 2/5x + 8/5 + 1 ⇒ y = - 2/5x + 13/5

line GD

y + 2 = 5/2(x - 4) ⇒ y = 5/2x - 10 - 2 ⇒ y = 5/2x - 12

Their graph and intersection point is given in the attached picture

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