The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is
Answer Details
The first step is to find the intersection point of the two lines y = 2x + 4 and y = 7 - x. To do this, we can set the two equations equal to each other and solve for x:
2x + 4 = 7 - x
3x = 3
x = 1
So, the intersection point is (1, 2).
Next, we can use the distance formula to find the distance between the point (4, 3) and the intersection point (1, 2):
distance = √((4 - 1)^2 + (3 - 2)^2) = √((3^2) + (1^2)) = √(9 + 1) = √10 = √(2 * 5) = √2 * √5 = 3√2.
So, the distance between the two points is 3√2.