Question

A car and a limo each drive along a straight road between two points. Using the points on a map that the city created, the car will start at (5, 7) and will stop at (–2, –7), while the limo will start at (3, –5) and will stop at (–4, 9).

What are the coordinates of the intersection that the car and the limo both drive through?

Answer 1

The path of the car and the limo are straight lines. To determine the equation of the lines of the paths, the slopes must be determined. Let m1 = slope of car m2 = slope of limo so, m1 = (7 + 7)/(5 + 2) = 2 m2 = (-5 -9)/(3+4) = -2 therefore the equations are car: 2x – y = 2(5) –(7) 2x – y = 3 Limo: 2x + y = 2(3) – 5 2x + y = 1 Solving the intersection of the equations (using a calculator) x = 1 y = -1

Answer 2

Answer:

(1,-1)

Step-by-step explanation:

Given,

The starting point of the car is (5,7) and end point of the car is (-2,-7),

So, the equation that represents the position of car,

$y-7=\frac{-7-7}{-2-5}(x-5)$

$y-7=\frac{-14}{-7}(x-5)$

$y-7=2(x-5)$

$y-7=2x-10$

$\implies 2x-y=3-----(1)$

Similarly, the start point of the limo is (3,-5) and end point of the limo is (-4,9),

So, the equation that represents the position of limo,

$y+5=\frac{9+5}{-4-3}(x-3)$

$y+5=\frac{14}{-7}(x-3)$

$y+5=-2(x-3)$

$y+5=-2x+6$

$2x+y=1----(2)$

Adding equation (1) and (2),

4x = 4 ⇒ x = 1

From equation (1),

2(1) - y = 3 ⇒ -y = 3 - 2 ⇒ -y = 1 ⇒ y = -1

Hence, the intersection point of line (1) and (2) is (1,-1).