In this chapter, we provide RD Sharma Class 10 Ex 14.5 Solutions Chapter 14 Coordinate Geometry for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 10 Ex 14.5 Solutions Chapter 14 Coordinate Geometry pdf, Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 14 |

Chapter Name | Coordinate Geometry |

Exercise | 14.5 |

Category | RD Sharma Solutions |

**RD Sharma Solutions for Class 10 Chapter** **14**** Coordinate Geometry** Ex 14.5 Download PDF

**Coordinate Geometry**Ex 14.5 Download PDF

**Chapter 14: Coordinate Geometry Exercise – 14.5**

**Question: 1**

Find the area of a triangles whose vertices are

(i) (6, 3), (-3, 5) and (4, – 2)

(ii) [(at_{1}^{2}, at_{1}),( at_{2}^{2}, 2at_{2})( at_{3}^{2}, 2at_{3})]

(iii) (a, c + a), (a, c) and (-a, c – a)

**Solution:**

(i) Area of a triangle is given by

1/2[x_{1}(y_{2 }– y_{3}) + x_{2}(y_{3 }– y_{1}) + x_{3}(y_{1 }+ y_{2})]

Here, x_{1 }= 6,y_{1 }= 3, x_{2} = -3, y_{2 }= 5, x_{3 }= 4,y_{3} = -2]

Let A(6, 3), B(-3, 5) and C(4,-2) be the given points

Area of ∆ABC = 1/2 [6(5+2)+(-3)(- 2 -3)+ 4(3 – 5)]

=1/2 [6 × 7- 3 × ( – 5) + 4( – 2)]

= 1/2[42 +15 – 8]

= 49/2 sq. units

(ii) Let A = (x_{1}, y_{1}) = (at_{1}^{2}, 2at_{1})

B = (x_{2},y_{2}) = (at_{2}^{2}, 2at_{2})

= (x_{3}, y_{3}) = (at_{3}^{2}, 2at_{2}) be the given points.

The area of ∆ABC

(iii) Let A = (x_{1},y_{1}) = (a, c + a)

B = (x_{2}, y_{2}) = (a, c)

C = (x_{3}, y_{3}) = (- a, c **– **a) be the given points

The area of ∆ABC

= 1/2[a ( – {c – a}) + a(c – a – (c + a)) +( – a)(c + a – a)]

= 1/2 [a(c – c + a) + a(c – a – c – a) – a(c + a – c)]

= 1/2[a × a + ax( – 2a) – a × a]

= 1/2[a^{2 }– 2a^{2 }– a^{2}]

= 1/2×(-2a)^{2}

= – a^{2}

**Question: 2**

Find the area of the quadrilaterals, the coordinates of whose vertices are

(i) (-3, 2), (5, 4), (7, -6) and (-5,- 4)

(ii) (1, 2), (6, 2), (5, 3) and (3, 4)

(iii) (-4, -2), (-3, -5), (3, -2), (2, 3)

**Solution:**

(i) Let A(-3, 2), B(5, 4), C(7,- 6) and D ( -5, – 4) be the given points.

Area of ∆ABC

= 1/2[-3(4 + 6) + 5(- 6 – 2) + 7(2 – 4)]

= 1/2[-3×1 + 5×(-8) + 7(-2)]

= 1/2[- 30 – 40 -14]

= – 42

But area cannot be negative

∴ Area of ∆ADC = 42 square units

Area of ∆ADC

= 1/2[-3( – 6 + 4) + 7(- 4 – 2) + (- 5)(2 + 6)]

= 1/2[- 3( – 2) + 7(- 6) – 5 × 8]

= 1/2[6 – 42 – 40]

= 1/2 × – 76

= – 38

But area cannot be negative

∴ Area of ∆ADC = 38 square units

Now, area of quadrilateral ABCD

= Ar. of ABC+ Ar of ADC

= (42 + 38)

= 80 square. Units

(ii) Let A(1, 2) , B (6, 2) , C (5, 3) and (3, 4) be the given points

Area of ∆ABC

= 1/2[1(2 – 3) + 6(3 – 2) + 5(2 – 2)]

= 1/2[ -1 + 6 × (1) + 0]

= 1/2[ – 1 + 6]

= 5/2

Area of ∆ADC

= 1/2[1(3 – 4) + 5(4 – 2) + 3(2 – 3)]

= 1/2[-1 × 5 × 2 + 3(-1)]

= 1/2[-1 + 10 – 3]

= 1/2[6]

= 3

Now, Area of quadrilateral ABCD

= Area of ABC + Area of ADC

(iii) Let A (- 4, 2), B( – 3, – 5), C (3,- 2) and D(2, 3) be the given points

Area of ∆ABC = 1/2|(- 4)(- 5 + 2) – 3(-2 + 2) + 3(- 2 + 5)|

= 1/2|(-4)(-3) – 3(0) + 3(3)|

= 21/2

Area of ∆ACD = 1/2|( – 4)(3 + 2) + 2( – 2 + 2) + 3( – 2 – 3)|

= 1/2|- 4(5) + 2(0) + 3(- 5)|= (- 35)/2

But area can’t neative, hence area of ∆ADC = 35/2

Now, of quadrilateral (ABCD) = ar(∆ABC) + ar(∆ADC)

Area (quadrilateral ABCD) = 21/2 + 35/2

Area (quadrilateral ABCD) = 56/2

Area (quadrilateral ABCD) = 28 square. Units

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