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WAEC Mathematics 2023 Paper

Question : 37

Total: 50

Write the name of a triangle with the vertices (1, -3), (6, 2) and (0,4)?

Solution:

Let A = (1, -3), B = (6, 2) and C = (0,4)

$d = \sqrt{ (y_2 - y_1)^2 + (x_2 - x_1)^2 }$

|AB| =

\sqrt{(2 - (-3))^2 + (6 - 1)^2}

\sqrt{(2 + 3)^2 + (6 - 1)^2}

\sqrt{5^2 + 5^2}

\sqrt{25 + 25}

\sqrt{50}

= 5

\sqrt{2}

units

|BC| =

\sqrt{(4 - 2)^2 + (0 - 6)^2}

\sqrt{2^2 + (-6)^2}

\sqrt{4 + 36}

\sqrt[4]{0}

= 2

\sqrt{10}

units

|AC| =

\sqrt{(4 - (-3)^2 + (0 - 1)^2}

\sqrt{(4 + 3)^2 + (0 - 1)^2}

\sqrt{7^2 + (-1)^2}

\sqrt{49 + 1}

\sqrt{50}

= 5

\sqrt{2}

units

Since two sides are equal (|AB| = |AC|), then the triangle is Isosceles.

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