Question

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k.

Answer 1

Solution

Points A, B and C are collinear.

Therefore,

½ [(k + 1)(2k + 3 – 5k) + 3k(5k – 2k) + (5k – 1)(2k – 2k – 3)] = 0

(k + 1)(3 – 3k) + 9k2 – 3(5k – 1) = 0

2k2 – 5k + 2 = 0

(k – 2)(2k – 1) = 0

k = 2, 1/2

Answer 2

Answer:

Joining BD, there are two triangles.

Area of quad ABCD = Ar △ABD + Ar △BCD

Ar △ABD = ½| (-5)(-5 - 5) + (-4)(5 - 7) + (4)(7 + 5) |

= 53 sq units

Ar △BCD = ½| (-4)(-6 - 5) + (-1)(5 + 5) + (4)(-5 + 6) |

= 19 sq units

Hence, area of quad ABCD = 53 + 19 = 72 sq units

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Explanation: