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.
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Answered by
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
Answered by
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
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