Question

40.
The point B is the image of A in the line x + y + 4 = 0 and C is the image of B in the line
2.x - y + 2 = 0.If A = (1, 2) then circumdiameter of triangle ABC is
A) 12
B) 10
C) 8
D) 5​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Concept:

Triangle is a figure which has 3 sides and 3 vertices.

It can be of three types based upon the classification of sides.

Given:

The point B is the image of A in the line x + y + 4 = 0

C is the image of B in the line 2x - y + 2 = 0

Find:

circumdiameter of triangle ABC

Solution:

B is the image of A(1,2) with respect to x+y+4=0

This means that:

(h-x₁)/a=(k-y₁)/b=-2(ax₁+by₁+c)/a²+b²

Which means that:

h-1=k-2=-7

This gives us the values:

h=-6 and k=-5

Therefore, we get the B point as (-6,-5).

C is the image of B with respect to 2x-y+2=0:

This means that:

(h-x₁)/a=(k-y₁)/b=-2(ax₁+by₁+c)/a²+b²

Which means that:

(h+6)/2=k+5=2

This gives us the values:

h=-2 and k=-7

Therefore, we get the C point as (-2,-7).

Now to find the circumdiameter of the triangle we will get the sides of the triangle by:

AB=√49+49=7√2

BC=2√5

AC=3√18

Slope of:

AB= 1

BC=1/2

AC= 3

R=abc/4Δ=(7√2×2√5×3√18)/4Δ= 63√5/Δ=12.

Therefore, we get the circumdiameter of the triangle as Option(A) 12.

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