Question 15 of 25intermediate🔧 ApplyNumerical3 marks

Plot point Z (5, −6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides.

Correct Answer

Point Z(5, -6) is plotted in Quadratic IV as its x-coordinate is positive and y-coordinate is negative. To construct a right-angled triangle IZN, let point I be (5, 0) on the x-axis and point N be (0, -6) on the y-axis. This makes angle Z a right angle.

Length of IZ: |0 - (-6)| = 6 units Length of ZN: |5 - 0| = 5 units Length of IN: Using Pythagoras theorem, IN = IZ2+ZN2\sqrt{IZ² + ZN²} = 62+52\sqrt{6² + 5²} = 36+25\sqrt{36 + 25} = 61\sqrt{61} units

(Answers may differ based on the choice of points I and N)

Exercise: END-OF-CHAPTER EXERCISES | Q: 4 | (Page 12)
For More Understanding

Explanation

The textbook context explicitly notes that answers may differ from person to person depending on the choice of the other two vertices. By selecting points I and N on the axes aligned with Z's coordinates, the legs of the right-angled triangle become parallel to the axes. This simplifies the calculation of side lengths to just finding the difference in coordinates, avoiding the distance formula which is appropriate for this introductory stage of Coordinate Geometry in Class 9.

Solution Steps

  1. Step 1: Plot point Z(5, -6) in Quadrant IV.

  2. Step 2: Choose points I(5, 0) and N(0, -6) to form a right-angled triangle IZN at Z.

  3. Step 3: Calculate vertical side IZ = |0 - (-6)| = 6 units.

  4. Step 4: Calculate horizontal side ZN = |5 - 0| = 5 units.

  5. Step 5: Calculate hypotenuse IN = 62+52\sqrt{6² + 5²} = 61\sqrt{61} units.

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