Question

8. The two vertices of a right-angled triangle ABC, right-
angled at A are A(2, 4) and B(6, 4). Plot these two
points on a Cartesian plane and find the coordinates
of the possible points C, given that the height of the
triangle ABC is 5 units.​

Answer 1

Answer:

Let the points be A(2,2),B(2,1),C(5,2).

Distance between two points (x

1

,y

1

) and (x

2

,y

2

) can be calculated using the formula

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

Hence, Length of side AB =

(−2−2)

2

+(1+2)

2

=

16+9

=

25

=5

Length of side BC ==

(5+2)

2

+(2−1)

2

=

49+1

=

50

Length of side AC =

(5−2)

2

+(2+2)

2

=

9+16

=

25

=5

Since, (

50

)

2

=(

25

)

2

+(

25

)

2

,

=>BC

2

=AB

2

+AC

2

Hence, the triangle has a right angle at A, with AB and AC as base and height.

Area of the triangle ABC =

2

1

×base×height=

2

1

×5×5=

2

25

sq units.