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irina [24]
2 years ago
8

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) an

d D (6.3). Also find the equations AG, BD and the point of intersection of AB, GD​
Mathematics
1 answer:
Mumz [18]2 years ago
5 0

Answer:

  • See below

Step-by-step explanation:

<u>Find the slope of each line:</u>

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

<u>The product of the slopes is - 1, hence the lines are perpendicular:</u>

  • - 2/5 * 5/2 = - 1

Equation of each line

<u>Line AB</u>

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

<u>line GD</u>

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

<em>Their graph and intersection point is given in the attached picture</em>

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