then/now you proved that two lines are parallel using angle relationships. find the distance between...
TRANSCRIPT
![Page 1: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/1.jpg)
You proved that two lines are parallel using angle relationships.
• Find the distance between a point and a line.
• Find the distance between parallel lines.
![Page 2: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/2.jpg)
• equidistant
![Page 3: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/3.jpg)
![Page 4: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/4.jpg)
![Page 5: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/5.jpg)
![Page 6: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/6.jpg)
![Page 7: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/7.jpg)
Distance Between Parallel Lines
Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 1, respectively.
You will need to solve a system of equations to find the endpoints of a segment that is perpendicular to both a and b. From their equations,we know that the slope of line a and line b is 2.
Sketch line p through they-intercept of line b, (0, –1),perpendicular to lines a and b.
a b
p
![Page 8: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/8.jpg)
Distance Between Parallel Lines
Step 1
Use the y-intercept of line b, (0, –1), as one of the endpoints of the perpendicular segment.
Write an equation for line p. The slope of p is the
opposite reciprocal of
Point-slope form
Simplify.
Subtract 1 from each side.
![Page 9: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/9.jpg)
Distance Between Parallel Lines
Use a system of equations to determine the point of intersection of the lines a and p.
Step 2
Substitute 2x + 3 for y in the second equation.
Group like terms on each side.
![Page 10: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/10.jpg)
Distance Between Parallel Lines
Simplify on each side.
Multiply each side by .
Substitute for x in the
equation for p.
![Page 11: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/11.jpg)
Distance Between Parallel Lines
Simplify.
The point of intersection is or (–1.6, –0.2).
![Page 12: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/12.jpg)
Distance Between Parallel Lines
Use the Distance Formula to determine the distance between (0, –1) and (–1.6, –0.2).
Step 3
Distance Formula
x2 = –1.6, x1 = 0, y2 = –0.2, y1 = –1
Answer: The distance between the lines is about 1.79 units.
![Page 13: Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bff91a28abf838cc00d0/html5/thumbnails/13.jpg)
A. 2.13 units
B. 3.16 units
C. 2.85 units
D. 3 units
Find the distance between the parallel lines a and b
whose equations are and ,
respectively.