What is the volume of this solid figure made with cubes?
1 answer:
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Answer:
a. Not perpendicular.
b. Perpendicular.
Step-by-step explanation:
We need to check whether the segments through the origin and the points listed perpendicular.
Product of slopes of two perpendicular lines is -1.
(a) The given points are (9,10) and (10,9).
Slope of line segment through (0,0) and (9,10) is
Slope of line segment through (0,0) and (10,9) is
Product of slopes is
Therefore, the line segments through the origin and the points (9,10) and (10,9) are not perpendicular.
(b) The given points are (9,6) and (4,-6).
Slope of line segment through (0,0) and (9,6) is
Slope of line segment through (0,0) and (4,-6) is
Product of slopes is
Therefore, the line segments through the origin and the points (9,6) and (4,-6) are perpendicular.
25 = 5*5 and 9 = 3*3, which we can exploit to write
so that this expression is actually a difference of squares. We can factorize this to get
and given that , we divide both sides by this to get