Which street is parallel to 2nd St.?

A dimensional graph with an x-axis and a y-axis is given. Six lines in names of street are drawn on it. 1st St. is drawn from (-7,7) to (-5.5,-5). 2nd St. is drawn from (-3.5,-7) to (-1.2,-5). 3rd Street is drawn is (1.4,7) to (5,-4). 4th Street is drawn from (2.8,7) to (7,-3.5). Elm Ave. is drawn from (-8,0.75) to (7,6.5). Main St. is drawn from (-7,-3.8) to (7,-2.25).

A. 1st St.
B. 3rd St.
C. 4th St.
D. Elm Ave.

1 answer

To determine which street is parallel to 2nd St., we need to find the slope of 2nd St. and then identify which other street has the same slope.

Finding the slope of 2nd St.: The coordinates for 2nd St. are:

  • Starting point: (-3.5, -7)
  • Ending point: (-1.2, -5)

The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates: \[ m = \frac{-5 - (-7)}{-1.2 - (-3.5)} = \frac{-5 + 7}{-1.2 + 3.5} = \frac{2}{2.3} \approx 0.87 \]

Finding the slopes of the other streets:

  1. 1st St. Points: (-7, 7) to (-5.5, -5) \[ m = \frac{-5 - 7}{-5.5 - (-7)} = \frac{-12}{1.5} = -8 \]

  2. 3rd St. Points: (1.4, 7) to (5, -4) \[ m = \frac{-4 - 7}{5 - 1.4} = \frac{-11}{3.6} \approx -3.06 \]

  3. 4th St. Points: (2.8, 7) to (7, -3.5) \[ m = \frac{-3.5 - 7}{7 - 2.8} = \frac{-10.5}{4.2} \approx -2.5 \]

  4. Elm Ave. Points: (-8, 0.75) to (7, 6.5) \[ m = \frac{6.5 - 0.75}{7 - (-8)} = \frac{5.75}{15} \approx 0.3833 \]

  5. Main St. Points: (-7, -3.8) to (7, -2.25) \[ m = \frac{-2.25 - (-3.8)}{7 - (-7)} = \frac{1.55}{14} \approx 0.1107 \]

Now we compare the slope of 2nd St. (approximately 0.87) with the slopes of the other streets:

  • 1st St.: -8 (not parallel)
  • 3rd St.: -3.06 (not parallel)
  • 4th St.: -2.5 (not parallel)
  • Elm Ave.: 0.3833 (not parallel)
  • Main St.: 0.1107 (not parallel)

None of these streets have the same slope as 2nd St. Therefore, based on the given options, none are parallel.

Based on the question and options, if we are forced to choose from the given options A, B, C, or D, none are correct. If we made an error in the assertion regarding slopes or if a condition applies that doesn't pertain to slopes being numerically identical, let me know!