# Geometry

Find the distance between the lines with the equations

y = 3/2x+4 and −3x+2y = −1.

1. 👍
2. 👎
3. 👁
1. y = 3/2x+4
2y = 3x + 8
3x - 2y + 8 = 0

-3x + 2y = -1
3x - 2y - 1 = 0 , so they are indeed parallel

pick any point on the first line,
e.g. let x = 2, then y = 7
so (2,7) lies on the first

distance from (2,7) to 3x - 2y - 1 = 0 is
|2(3) - 2(7) -1|/√(3^2 + (-2)^2)
= 9/√13
= appr 2.5

1. 👍
2. 👎

## Similar Questions

1. ### math

1. Find the length of the hypotenuse of a right triangle with legs of 9 cm and 12 cm A. 8 cm B. 21 cm C. 15 cm D. 225 cm the length of the hypotenuse of a right triangle with legs of 13 cm the length of one leg is 5 cm find the

2. ### Math

Which graph best represents the solution to the following pair of equations? (1 point) y = −x − 5 y = 2x + 4 A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines

3. ### calculus

Find equations for the lines that are tangent and normal to the graph of y = sinx + 3 at x = pi

4. ### math

What will the graph look like for a system of equations that has no solutions? A. The lines will be perpendicular. B. The lines cross at one point. C. Both equations will form the same line. D. The lines will be parallel. Is the

1. ### math

Consider the following system of equations. {y = 3x − 5 {y = −x + 7 a. Are the graphs of the two lines intersecting lines, the same line, or parallel lines? Explain your reasoning. b. How many solutions does the system have?

2. ### MATH PLS HELP CHECK ANSWERS

3. What is the rule for the function shown in the table? (1 point) x = -1, 0, 1, 2 y = -2, 1, 4, 7 A.y = 1/3x + 1 B.y = 3x + 1 C.y = 1/3x D.y = 1/2x + 1 4. What is the function rule for the following situation? rex paid \$20 for a

3. ### math

Find the slope of the lines that are (a) parallel lines (b) perpendicular lines to the lines passing through the pair of points (3, 4)(2,-1)

4. ### maths

P(6,3), Q(3,7), and R(4,2) are three points in a plane. A is the midpoint of QR and B is the foot of the perpendicular from Q to PR. Find;- (A) the cordinates of A; (B) the equations of the lines PA and QB; (C) the point of

1. ### algebra

Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x - 4y = -3 8x + 6y = -3

2. ### algebra

Given an equation of a line, find equations for lines parallel or perpendicular to it going through specified points. Find the appropriate equations and points from the table below. Simplify your equations into slope-intercept

3. ### Calculus

(A) Find the equations of the tangent lines to the circle x^2 +y^2=25 at the points where x=4. (B) Find the equations of the normal lines to this circle at the same points. (The normal line is perpendicular to the tangent line at

4. ### Geometry

Examine the two distinct lines defined by the following two equations in slope-intercept form. line ℓ: y=34x+6 line k: y=34x−7 Are lines ℓ and k parallel? Justify your response. 1.Yes, lines ℓ and k are parallel because