Question 626744: Hello, please help me solve:
A first line in the xy-plane is given by y= 2x-1 and a second line is given by
y= x+1.
a) find the coordinates of the point P of intersection of these two lines.
b) find the distance from the origin (0,0) to the point P.
Thank you so much!
Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website!
Hello, please help me solve:
A first line in the xy-plane is given by y= 2x-1 and a second line is given by
y= x+1.
a) find the coordinates of the point P of intersection of these two lines.
b) find the distance from the origin (0,0) to the point P.
Thank you so much!
Since the equations are non-parallel (different slopes) they will intersect each other. We can therefore say that since y = 2x - 1, and y = x + 1, then:
2x - 1 = x + 1
2x - x = 1 + 1
x = 2
y = 2(2) - 1 ----- Substituting 2 for x in equation
y = 4 - 1
y = 3
Since x = 2, and y = 3, then point of intersection of both lines, or P = ( , )
Drawing a diagram, you will see that the distance from the origin, (0, 0) to P (point of intersection) is represented as the hypotenuse of a right-triangle, with one leg measuring 2 units (on the x-axis), and another leg measuring 3 units (vertical and parallel to the y-axis), on the xy-plane.
With H being the length of the hypotenuse, we have:  ----  -----  ----- 
The distance from the origin (0, 0) to P (point of intersection), or coordinate point (2, 3) =  .
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