Question

18. (1) Find the equation of AC which is parallel to x-axis in the given figure. (ii) If slope of AB = 2, find the equation of AB. (iii ) Find the co-ordinates of A. (iv) Find the area of AABC.​

Answer 1

Answer:

(i) Coordinates of A(4,0)

(ii) Coordinates of A(4,0) and B(−2,3)

Length of AB=

(−2−4)

2

+(3−0)

2

=

36+9

=

45

=3

5

units.

Coordinates of A(4,0) and C(−2,−4)

Length of AC=

(−2−4)

2

+(−4−0)

2

=

36+16

=

52

=2

13

units.

(iii) Let the ratio be k:1

∴ Coordinates of P is (

m

1

+m

2

m

1

x

2

+m

2

x

1

,

m

1

+m

2

m

1

y

2

+m

2

y

1

)=(

k+1

−2k+4

,

k+1

−4k

)

Let coordinates of P is (x,y).

x=

k+1

−2k+4

0=

k+1

−2k+4

[as P lies on y-axis]

2k=4⇒k=2

Ratio =2:1

(iv) Equation of AC

Coordinates of A(4,0) and C(−2,−4)

y−0=

4+2

0+4

(x−4)

3y=2x−8

2x−3y−8=0

Answer 2

Answer:

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal AC

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1Now, the co-ordinates of the mid- point of AC is given by

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1Now, the co-ordinates of the mid- point of AC is given by(2(3−1),2(6+2))=(22,28)=(1,4)

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1Now, the co-ordinates of the mid- point of AC is given by(2(3−1),2(6+2))=(22,28)=(1,4)So, the equation of BD will be

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1Now, the co-ordinates of the mid- point of AC is given by(2(3−1),2(6+2))=(22,28)=(1,4)So, the equation of BD will bey−4=−1(x−1)

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1Now, the co-ordinates of the mid- point of AC is given by(2(3−1),2(6+2))=(22,28)=(1,4)So, the equation of BD will bey−4=−1(x−1)y−4=−x+1

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1Now, the co-ordinates of the mid- point of AC is given by(2(3−1),2(6+2))=(22,28)=(1,4)So, the equation of BD will bey−4=−1(x−1)y−4=−x+1x+y=5

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)Slope of AC(m1)=(−1−3)(2−6)=−4−4=1We know that, the diagonals of a rhombus bisect each other at the right angles.So, the diagonal BD is perpendicular to diagonal ACLet the slope of BD be m2Then, m1×m2=−1m2=(m1)−1=(−1)−1=−1Now, the co-ordinates of the mid- point of AC is given by(2(3−1),2(6+2))=(22,28)=(1,4)So, the equation of BD will bey−4=−1(x−1)y−4=−x+1x+y=5Thus, the equation of BD is x+y

Step-by-step explanation:

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