1.

Four lines are drawn on a coordinate plane to form trapezoid WXYZ. A coordinate grid with 4 lines. Line X W is drawn with point W at (negative 4, 1) and passes through (0, 2) with and (3, 3). Line Y X is drawn with point Y at (3, 0) and passes through (0, 3). Line Z W is drawn with point Z at (0, negative 3) and point W at (negative 4, 1). LIne Z Y is drawn with point Y at (3, 0) and point Z at (0, negative 3). Which statements are true about the lines? Select three options. Line WZ has the same slope as line XY. Line YX has a greater slope than line ZY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line YZ. Line XY has a lesser y-intercept than line XW.

Answer»

Given:

  1. Line XW is drawn with point W at (- 4, 1) and passes through (0, 2)
  2. Line YX is drawn with point Y at (3, 0) and passes through (0, 3)
  3. Line ZW is drawn with point Z at (0, - 3) and point W at (- 4, 1)
  4. Line ZY is drawn with point Y at (3, 0) and point Z at (0, - 3)

To find:

The correct optons out of -

  1. Line WZ has the same SLOPE as line XY.
  2. Line YX has a greater slope than line ZY.
  3. Line XW has a lesser slope than line YZ.
  4. Line ZW has the same y-intercept as line YZ.
  5. Line XY has a lesser y-intercept than line XW.

Answer:

The equation of a STRAIGHT line with coordinates (x1,y1), (x2,y2) is -

y - y1 = \frac{y2 - y1}{x2 - x1} (x - x1)   -(1)

where the slope is [y2 - y1/ (x2 - x1)]

Thus from equation (1), the equations of the lines are -

  • XW - y - 1 = (1/2) (x +4)
  • XY - y = -1 (x - 3)
  • ZW - y + 3 = -1 (x)
  • ZY - y = 1 (x - 3)

Thus, the correct options are -

Line WZ has the same slope as line XY.

Line XW has a lesser slope than line YZ.

Line ZW has the same y-intercept as line YZ.

Line XY has a lesser y-intercept than line XW


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