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Shortcut Tricks: Coordinate Geometry Video Lecture | Quantitative for GMAT

FAQs on Shortcut Tricks: Coordinate Geometry Video Lecture - Quantitative for GMAT

1. What are the key properties of a right-angled triangle?

Ans. A right-angled triangle has one angle measuring 90 degrees. The sides opposite the right angle are known as the hypotenuse, while the other two sides are called the legs. The Pythagorean theorem applies, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

2. How can I determine the vertices of a right-angled triangle using coordinates?

Ans. To determine the vertices of a right-angled triangle using coordinates, identify three points in a coordinate plane. You can then check the slopes of the lines formed by these points. If the product of the slopes of two lines is -1, the triangle formed by those points is right-angled at the vertex where the two lines meet.

3. What is the easiest way to verify if a triangle is right-angled using its side lengths?

Ans. To verify if a triangle is right-angled using its side lengths, apply the Pythagorean theorem. If you have sides a, b, and c (where c is the longest side), check if a² + b² = c². If this equation holds true, then the triangle is right-angled.

4. Can the vertices of a right-angled triangle be expressed in terms of integer coordinates?

Ans. Yes, the vertices of a right-angled triangle can be expressed in terms of integer coordinates. For example, the vertices (0,0), (3,0), and (0,4) form a right-angled triangle with integer coordinates. As long as the Pythagorean theorem holds, integer coordinates can define a right-angled triangle.

5. What is the significance of the right angle in a right-angled triangle?

Ans. The right angle in a right-angled triangle is significant because it defines the triangle's classification and allows the use of specific properties and theorems, such as the Pythagorean theorem. The right angle also helps in calculating the area and perimeter of the triangle and is fundamental in trigonometry.

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Oct 02, 2025 Last updated

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	Quantitative for GMAT 121 videos\|148 docs\|111 tests

Quantitative for GMAT

121 videos|148 docs|111 tests

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