Shape and Space 1
4 marks · HardTriangle ABC has vertices at A(2,3), B(6,3), and C(2,8).
Calculate the lengths of each side of the triangle.
Determine the type of triangle (by its sides).
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) AB = 4, AC = 5, BC = \sqrt{41}\approx6.4 · must show AB = 4, AC = 5, BC = 6.4
(b) Scalene · must show All sides different
Must show: AB = 4, AC = 5, BC = \sqrt{(6-2)^2 + (3-8)^2} = \sqrt{16+25} = \sqrt{41}\approx6.4, Triangle is scalene (all sides different)
Common mistakes: Incorrect use of distance formula; Misclassifying as isosceles
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Marking points
M1 (a) · 1 mark · Uses distance formula correctly for two sides
A1 (a) · 1 mark · All three correct lengths (accept rounded BC = 6.4)
B1 (b) · 2 marks · Correct classification as scalene with clear justification (all sides different) (follow-through)
Worked solution
AB = |6-2| = 4
AC = |8-3| = 5
BC = \sqrt{(6-2)^2 + (3-8)^2} = \sqrt{16+25} = \sqrt{41}\approx 6.4
Since all sides are different, triangle ABC is scalene.