distance between X and y(3,7) and (-3,4) in
Answers
Answer:
The closest distance between a point and a line is the line segment perpendicular to the line with endpoints on the line and the point.
The slope of the original line (line 1) is 4. Therefore, the slope of the other line (line 2) is the negative reciprocal, -1/4.
We know that it passes through (5, 7). We can use point-slope form to solve for the equation of the line.
y - y_1 = m (x - x_1)
y - 7 = -1/4 (x - 5)
y - 7 = -x/4 + 5/4
y = -x/4 + 33/4
Using this equation, we can find the intersection of lines 1 and 2, the point on the line closest to the point.
y = -x/4 + 33/4
y = 4x + 3
-x/4 + 33/4 = 4x + 3
17x/4 = 21/4
x = 21/17
y = 4(21/17) + 3 = 135/17
Solution: (21/17, 135/17)
The two points we have are (21/17, 135/17) and (5, 7). Let’s use the Pythagorean Theorem to solve.
length = |sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)|
= sqrt((5 - 21/17)^2 + (7 - 135/17)^2)
= sqrt((64/17)^2 + (-16/17)^2)
= sqrt((4906/289) + (256/289))
= sqrt(5612/289)
Which gives an answer of around 4.226297634514 units.