Answer:
- scalene
- not a right triangle
Explanation:
You want a graph and a description of the triangle whose vertices are Q(2, 2), R(4, 8), and S(8, 5).
Graph
See the attachment for the correct graph. Plotting points on a graph should be no mystery: the first coordinate tells you how far to the right of the y-axis; the second coordinate tells you how far up from the x-axis. (The coordinates are (right, up).)
Side lengths
You can look at the differences between coordinate pairs to get an idea whether sides are the same length. Or you can go to the trouble to actually figure out the lengths.
R -Q = (4-2, 8-2) = (2, 6)
S -R = (8-4, 5-8) = (4, -3)
Q -S = (2-8, 2-5) = (-6, -3)
The ratios of the y-difference to the x-difference are ...
QR: 6/2 = 3
RS: -3/4
SQ: -3/-6 = 1/2
None of these is the opposite reciprocal of another, so no segments are perpendicular. The triangle is not a right triangle.
You can look at the sums of squares of these number to get an idea about length relationships:
QR² = 2² +6² = 40
RS² = 4² +(-3)² = 25
SQ² = (-6)² +(-3)² = 45
These are all different, so the triangle is scalene.
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Additional comment
You can tell whether the triangle is acute, right, or obtuse by looking at the value of the expression a²+b²-c², where a, b, c are the side lengths from smallest to largest. Here, that value is 25+40-45 = 20. It is greater than 0, so the triangle is acute. (=0: right; <0: obtuse)
Lines with opposite reciprocal slopes are perpendicular. For example, a line with a slope of -3/4 is perpendicular to one with a slope of 4/3.
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