Connecting algebra and geometry through coordinates

Practice sheet

Fresh questions from the whole chapter, to do on paper.

New questions

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  1. Find the distance between (−1,−3)(-1, -3) and (2,1)(2, 1).
  2. Tap the midpoint of the segment from (−6,−5)(-6, -5) to (−4,−1)(-4, -1).
  3. Find the exact distance between (0,−2)(0, -2) and (1,−4)(1, -4).
  4. A line has slope 1/81/8. Find the slope of a line perpendicular to it.
  5. Are the lines y=6x+1y = 6x + 1 and y=−16x+5y = -\tfrac{1}{ 6 }x + 5 parallel, perpendicular or neither?
    1. Perpendicular: the product of the slopes is −1
    2. Parallel
    3. Neither
  6. Find the slope of the line through (0,5)(0, 5) and (−5,−3)(-5, -3).
  7. Find the yy-intercept of the line parallel to y=−3x+−1y = -3x + -1 through (−3,−5)(-3, -5).
  8. Find the yy-intercept of the line perpendicular to y=4xy = 4x through (−3,−3)(-3, -3).
  9. Write the line with slope 33 through (4,−1)(4, -1): enter the right-hand side of y=…y = \ldots

Answers

  1. 55
  2. (−5,−3)(-5, -3)
  3. 5\sqrt{5}
  4. −8-8
  5. Perpendicular: the product of the slopes is −1
  6. 85\frac{8}{5}
  7. −14-14
  8. −154- \frac{15}{4}
  9. 3x−133 x - 13