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

Step 1: Analyze the question We need to classify the triangle by finding the lengths of its sides using the distance formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Step 2: Label the points A(1, −3), B(6, 2), C(0, 4)

Step 3: Compute the side lengths

• AB² = (6 − 1)² + (2 − (−3))² = 25 + 25 = 50, so AB = √50 ≈ 7.07
• BC² = (0 − 6)² + (4 − 2)² = 36 + 4 = 40, so BC = √40 ≈ 6.32
• AC² = (0 − 1)² + (4 − (−3))² = 1 + 49 = 50, so AC = √50 ≈ 7.07

Step 4: Compare AB = AC = √50, while BC = √40 is different. So exactly two sides are equal, which makes the triangle isosceles.

Check for a right angle: Does the sum of the squares of the two smaller sides equal the square of the largest? 40 + 50 = 90 ≠ 50, so no. In fact, no combination works (50 + 50 = 100 ≠ 40). So it is not right-angled.

It is also not equilateral, since the sides are not all equal.

Note on options: Strictly, a triangle with two equal sides is not scalene (scalene means all sides different), so A is out.

Exam tip: For "name the triangle" questions with coordinates, compute the squared distances (skip the square roots). Compare them: all equal gives equilateral, two equal gives isosceles, and if a² + b² = c² it is right-angled.