SOLUTION: A, B, C and D are points (-5, 2), (2, 3), ( -1, -6) and (3, 10) respectively. Find the coordinates of the point M where AD and BC intersect

Algebra ->  Coordinate-system -> SOLUTION: A, B, C and D are points (-5, 2), (2, 3), ( -1, -6) and (3, 10) respectively. Find the coordinates of the point M where AD and BC intersect      Log On


   

Question 1196131: A, B, C and D are points (-5, 2), (2, 3), ( -1, -6) and (3, 10) respectively. Find the coordinates of the point M where AD and BC intersect
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


intersection of the AD and BC will be where their extensions intersect
so we need equations of the lines that containing AD and BC
use endpoints of the line segment AD and find equation
slope is m=%2810-2%29%2F%283-%28-5%29%29=8%2F8=1
use point slope form to find equation

y-y1=m%28x-x1%29
plug in a slope and point D(-5, 2)
y-2=1%28x-%28-5%29%29
y-2=x%2B5
y=x%2B5%2B2
y=x%2B7 ... ...eq.1
so we have an equation of a line that contains A and D

now find a line that contains B and C

(2, 3), ( -1, -6)

slope is m=%28-6-3%29%2F%28-1-2%29=-9%2F-3=3

use point slope form to find equation

y-y1=m%28x-x1%29
plug in a slope and point (2, 3)
y-3=3%28x-2%29
y-3=3x-6
y=3x-6%2B3
y=3x-3... ...eq.2
so we have an equation of a line that contains B and C
the point M will be where these lines intersect

equal the right sides of the eq.1 and eq.2
x%2B7=3x-3
3%2B7=3x-x
10=2x
x=5

now find y
y=3%2A5-3... ...eq.2
y=12
the point M will be at (5, 12)

let see it all on a graph