4. Two lines passing through the point (2, 3) makes an
angle 45" . If the slope of one of the line 2
find the slope of the other line
Answers
Answer:
2 lines passing through P (2,3) make an angle of 45 degrees. If the slope of L1 is 2, what is the slope of the other line.
One line (L1) passing through P (2,3) has a slope of 2. Its equation will be
y = mx+c, or
3 = 2*2+c, or
c = -1. So the equation of the line (L1) is y = 2x-1 …(1)
The slope of L1 is arctan 2 or 63.43494882 deg. If line L2 makes an angle of 45 deg with L1 its slope could be 63.43494882 - 45 =18.43494882 deg and tan 18.43494882 = (1/3) or 63.43494882 + 45 = 108.43494882 deg and tan 108.43494882 = (-3)
So line L2 can have the slope as (1/3) or (-3). The equation of the lines will be
3 = (1/3)*2+c, or
3–2/3 = 1/3 = c, L2 becomes y = (1/3)x+1/3 or 3y-x = 1 or
3 = (-3)*2+c, or
9 = c, Thus L2 becomes y+3x = 9.
Answer: The line L2 could be either 3y-x = 1 whose slope is (1/3) or y+3x = 9 whose slope is (-3)
Answer:
2 lines passing through P (2,3) make an angle of 45 degrees. If the slope of L1 is 2, what is the slope of the other line.
Step-by-step explanation:
One line (L1) passing through P (2,3) has a slope of 2. Its equation will be
y = mx+c, or
3 = 2*2+c, or
c = -1. So the equation of the line (L1) is y = 2x-1 …(1)
The slope of L1 is arctan 2 or 63.43494882 deg. If line L2 makes an angle of 45 deg with L1 its slope could be 63.43494882 - 45 =18.43494882 deg and tan 18.43494882 = (1/3) or 63.43494882 + 45 = 108.43494882 deg and tan 108.43494882 = (-3)
So line L2 can have the slope as (1/3) or (-3). The equation of the lines will be
3 = (1/3)*2+c, or
3–2/3 = 1/3 = c, L2 becomes y = (1/3)x+1/3 or 3y-x = 1 or
3 = (-3)*2+c, or
9 = c, Thus L2 becomes y+3x = 9.
Answer: The line L2 could be either 3y-x = 1 whose slope is (1/3) or y+3x = 9 whose slope is (-3)