Question 4 of 18intermediate🔧 ApplyShort Answer2 marks

Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

Correct Answer

Yes, the points (5, -2), (6, 4) and (7, -2) form an isosceles triangle.

Let A(5, -2), B(6, 4) and C(7, -2) be the given points.

AB = √[(5-6)² + (-2-4)²] = √[1 + 36] = 37\sqrt{37}

BC = √[(6-7)² + (4-(-2))²] = √[1 + 36] = 37\sqrt{37}

AC = √[(5-7)² + (-2-(-2))²] = √[4 + 0] = 2

Since AB = BC = 37\sqrt{37}, two sides of the triangle are equal. Therefore, the given points form an isosceles triangle.

Exercise: EXERCISE 7.1 | Q: 4 | (Page 7)
For More Understanding

Explanation

This question tests the application of the distance formula to determine the type of triangle. Students need to calculate all three sides and check if any two are equal. The distance formula PQ = √[(x₁-x₂)² + (y₁-y₂)²] is used. An isosceles triangle has at least two equal sides. Here, AB = BC, confirming the triangle is isosceles.

Solution Steps

  1. Step 1: Label the points as A(5, -2), B(6, 4), C(7, -2)

  2. Step 2: Calculate AB using distance formula = 37\sqrt{37}

  3. Step 3: Calculate BC using distance formula = 37\sqrt{37}

  4. Step 4: Calculate AC using distance formula = 2

  5. Step 5: Compare sides - AB = BC, hence isosceles triangle

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