Question

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.

Answer 1

Answer:

• x = 11.2
• y = - 19.4

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)