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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:

Concept:

Classify the triangle by comparing the lengths of its three sides.

Explanation:

Let

\mathrm{A} = (1,-3)

\mathrm{B} = (6,2)

and

\mathrm{C} = (0,4)

Use the distance formula:

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

Calculate

|\mathrm{AB}|

|\mathrm{AB}| = \sqrt{(6 - 1)^2 + (2 - (-3))^2}

= \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \ \text{units}

Calculate

|\mathrm{BC}|

|\mathrm{BC}| = \sqrt{(0 - 6)^2 + (4 - 2)^2}

= \sqrt{(-6)^2 + 2^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10} \ \text{units}

Calculate

|\mathrm{AC}|

|\mathrm{AC}| = \sqrt{(0 - 1)^2 + (4 - (-3))^2}

= \sqrt{(-1)^2 + 7^2} = \sqrt{1 + 49} = \sqrt{50} = 5\sqrt{2} \ \text{units}

Now compare the side lengths:

|\mathrm{AB}| = |\mathrm{AC}| = 5\sqrt{2} \ \text{units}

Two sides are equal, so the triangle has two congruent sides.

Answer:

The triangle is an isosceles triangle. Option B.

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