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Line A passes through the points (-5,-8) and (4,19). Line B passes through the points (3,-3) and (-6,15). Find the coordinates of the point where line A intersects line B.

User Ritikesh
by
8.0k points

1 Answer

4 votes

Answer:

  • x = 11.2
  • y = - 19.4

Step-by-step explanation:

To find, analytically, the coordinates of the point where line A intersects line B, you find the equation of each line and solve a system of equations, whose solution will be the coordinates of suct intersection point.

1. Line A

  • point (-5, - 8)
  • point (4, 19)
  • equation:

slope: (19 - (-8) ) / (4 - (- 5)) = (19 + 8) / (4 + 5) = 27 / 6 = 3

point-slope equation: y - 4 = 3 ( x - 19)

clear y: y = 3x - 57 + 4

y = 3x - 53

2. LIne B

  • point ( 3, -3)
  • point (- 6, 15)
  • equation:

slope: ( 15 - (-3)) / (-6 - 3) = (15 + 3) / (-9) = 18 / (-9) = - 2.

point-slope equation: y + 3 = - 2( x - 3)

clear y: y = - 2x + 6 - 3

y = - 2x + 3

3. Solve the system (find the intersection point)

  • y = 3x - 53 . . . equation (1)
  • y = - 2x + 3 . . . equation (2)

Subtract equation (2) from equation (1)

  • 0 = 3x + 2x - 53 - 3
  • 56 = 5x
  • x = 56 / 5 = 11.2

Substitute x = 11.2 into equation (2)

  • y = -2 (11.2) + 3 = -19.4

Intersection point (11.2, -19.4)

User FAISAL
by
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