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Slope from Two Points & Glide Ratio Word Problem (Foundations & Pre-Calculus 10)

  • Writer: Tyler Buffone
    Tyler Buffone
  • 5 days ago
  • 2 min read
Silhouette of a plane flying against a vibrant, abstract sky with swirling red, orange, yellow, and teal patterns, creating a dynamic mood.

Page 341, Question 18 (Foundations and Pre-Calculus Mathematics 10, Pearson, 2010 Edition)


a) For each pair of labeled points below, sketch the line that passes through them and compute its slope.


  • B(0, 3) and C(5, 0)

  • D(0, -3) and C(5, 0)

  • D(0, -3) and E(-5, 0)

  • B(0, 3) and E(-5, 0)


b) Compare the four slope values from part (a). What pattern or relationship do you notice among them?


Solution a)


To draw a line through two pairs of points, plot them on a coordinate grid and connect the points using a straight line. See the following four images containing graphs created with Desmos (desmos.com) that show these lines.


i) B(0, 3) and C(5, 0)


Slope = (rise / run) = (0 - 3) / (5 - 0) = -3/5


Graph with a green diagonal line crossing the y-axis at (0, 3) and x-axis at (5, 0). Points marked in red and blue on the grid.

ii) D(0, -3) and C(5, 0)


Slope = (0 - (-3)) / (5 - 0) = (0 + 3) / 5 = 3/5


Graph with a purple line crossing through points (0, -3) in red and (5, 0) in blue on a grid. Axis numbers are visible.

iii) D(0, -3) and E(-5, 0)


Slope = (0 - (-3)) / (-5 - 0) = (0 + 3) / (-5) = -3/5


Blue line on graph with points labeled (-5, 0) and (0, -3). Line crosses grid, highlighting intersection and slope. Neutral mood.

iv) B(0, 3) and E(-5, 0)


Slope = (0 - 3) / (-5 - 0) = (-3) / (-5) = 3/5


Graph showing a diagonal purple line with points labeled (-5, 0) and (0, 3) on a grid background.

Solution b)


Recall that the slopes were as follows:


i) Slope BC = -3/5

ii) Slope CD = 3/5

iii) Slope DE = -3/5

iv) Slope BE = 3/5


Therefore, slope BC = slope DE and slope CD = Slope BE.

Therefore, slope BC and slope DE are opposite to slope CD and slope BE. They share the same magnitude, but they differ in sign. That is, despite having the same number, slope BC and slope DE are negative whereas slope CD and slope BE are positive.


Page 343, Question 29 (Foundations and Pre-Calculus Mathematics 10, Pearson, 2010 Edition)


In 1983, a Boeing 767 flying across Canada famously ran out of fuel due to a unit-conversion error. Imagine a similar situation where the plane must glide to safety at a constant descent rate.


  • During one part of the flight, the altitude decreases from 7000 m to 5500 m while the plane travels 18 km horizontally.


  • Later, the plane is at an altitude of 2600 m and still 63 km away from Winnipeg.


Assuming the plane continues gliding at the same constant rate of descent, determine whether it has enough altitude to reach Winnipeg before touching the ground. Show your reasoning and clearly explain your conclusion.


Solution


From the given glide segment:


Vertical drop: 7,000 - 5,500 = 1,500 m

Horizontal distance: 18 km = 18,000 m


Glide slope (drop per horizontal metre):


drop / run = 1,500 / 18,000 = 1/12


So the plane loses 1 m of altitude for every 12 m horizontally.


With altitude 2,600 m remaining, the maximum horizontal distance it could glide is


2,600 x 12 = 31,200 m = 31.2 km


But Winnipeg is 63 km away, which is greater than 31.2 km


Conclusion: No, the plane could not reach Winnipeg at that glide ratio. It would run out of altitude roughly 63 - 31.2 = 31.8 km before reaching the city.



Need help mastering slopes and linear equations? If you’re in Winnipeg and looking for a tutor, Tutor Advance provides expert one-on-one support!



 
 
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