Question

prove theorem of areas of similar triangles, use the ratio: LM/XY= MN/YZ= LN/XZ​

Answer 1

Answer:

Correct option is

A

1

Let Δ=

∣

∣

∣

∣

∣

∣

∣

∣

l

1

l

2

l

3

m

1

m

2

m

3

n

1

n

2

n

3

∣

∣

∣

∣

∣

∣

∣

∣

Δ

2

=

∣

∣

∣

∣

∣

∣

∣

∣

l

1

l

2

l

3

m

1

m

2

m

3

n

1

n

2

n

3

∣

∣

∣

∣

∣

∣

∣

∣

×

∣

∣

∣

∣

∣

∣

∣

∣

l

1

l

2

l

3

m

1

m

2

m

3

n

1

n

2

n

3

∣

∣

∣

∣

∣

∣

∣

∣

Multiplying row by row

=

∣

∣

∣

∣

∣

∣

∣

∣

l

1

2

+m

1

2

+n

1

2

l

1

l

2

+m

1

m

2

+n

1

n

2

l

1

l

3

+m

1

m

3

+n

1

n

3

l

1

l

2

+m

1

m

2

+n

1

n

2

l

1

2

+m

2

2

+n

2

2

l

2

l

3

+m

2

m

3

+n

2

n

3

l

1

l

3

+m

1

m

3

+n

1

n

3

l

2

l

3

+m

2

m

3

+n

2

n

3

l

3

2

+m

3

2

+n

3

2

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

1

0

0

0

1

0

0

0

1

∣

∣

∣

∣

∣

∣

∣

∣

using given conditions.

⇒Δ

2

=1

∴Δ=±1

∴k=1