i have a problem on my homework that says find the distance between the pair of parallel lines. it gives me y=2x + 2 and y=2x - 3
2007-10-18 11:46:50 · 5 answers · asked by smart_blonde9112 1 in Science & Mathematics ➔ Mathematics
Put the equations into standard form and use the distance formula. Then choose a point on one line and calculate the distance to the other line.
Pick a point on the first line.
y = 2x + 2
A point on the first line is P(0,2).
Measure the distance from P to the second line.
y = 2x - 3
2x - y - 3 = 0
distance = |2*0 - 1*2 - 3| / √[2² + (-1)²] = 5/√5 = √5
2007-10-18 12:13:42 · answer #1 · answered by Northstar 7 · 2⤊ 4⤋
Hey y'all. I don't think 5 is the answer. That's the vertical distance between the lines, but it's not the distance between them. That's going to be a number less than 5, that is the length of a line segment that goes through both those lines at right angles.
There's some trig to do here. I'll work on it more when I get home....this is pretty tricky. What level Math is this?
***Okay, I think I got it! But I used a more difficult strategy than the 2 below me.
I drew a triangle between the two lines with the vertical leg (known) as the hypotenuse. Then I made a triangle below it with the horizonal leg as 1 and the vertical leg as 2 (slope) I found the small angle of that triangle
Arctan(2)
and then found the angle of the triangle between the lines.
90 degrees - Arctan(2)
Then found the length of the missing leg of the triangle between the lines
sin(90 deg - arctan(2)) * 5 = 2.24
And THAT is how NOT to do that math problem!
2007-10-18 12:01:22 · answer #2 · answered by Eric P 6 · 3⤊ 3⤋
Think about what the problem is asking........what is the distance between two parallel lines. Well parallel lines of the equation you give has a slope of 2. So you have one line with a slope of 2 at a y intercept of 2 and the other with a slope of 2 and the y intercept of -3. Being that 2 is above the x axis and -3 is below the x-axis the distance is 5
2007-10-18 11:58:07 · answer #3 · answered by ? 3 · 0⤊ 7⤋
The slope is 2 and y1 crosses x at y1(0)=2 and y2 crosses x at y2(0)=-3. The distance is 5 times cos(arctang(2)) = 2.23.
2007-10-18 12:08:33 · answer #4 · answered by Dracula 2 · 2⤊ 1⤋
Distance is
d = |2x+2 - 2x +3| = 5 units
2007-10-18 11:53:46 · answer #5 · answered by Anonymous · 0⤊ 6⤋