Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1st Question: a. 4/5

2nd Question: c. {(-1, 1), (-4, 5), (-1, 5)}

3rd Question: a, 12

Explanation:

1st Question:

Similarity ratio scale factor of the triangle can be easily found by dividing the respective corresponding sides of similar triangle.

`\tt (8)/(10)=(4)/(5)\\\\\tt (12)/(15)=(4)/(5)`

Therefore, Similarity ratio scale factor is a. 4/5

`\hrulefill`

2nd Question:

Coordinates of triangle (1,1), (5,4) and (5,1) is congruent triangle having coordinates (-1, 1), (-4, 5), (-1, 5).

Look at the picture respective side are equal:

• KL=AB
• LM=BC
• KM= AC

They are congruent by SSS axiom.

Therefore, the answer is c. {(-1, 1), (-4, 5), (-1, 5)}

`\hrulefill`

3rd question:

Given:

`\tt \triangle ABC \sim \triangle LMN`

Since the side of similar triangle are proportional.

So,

`\tt (LM)/(AB)=(LN)/(AC)`

substituting value

`\tt (10)/(5)=(3x+3)/(x+5)`

`\tt (2)/(1)=(3x+3)/(x+5)`

Doing criss cross multiplication.

2(x+5)=3x+3

opening bracket

2x+10=3x+3

subtracting both side by 2x.

10=3x-2x+3

10=x+3

subtracting both side by 3

10-3=x

x=7

Therefore, Length of AC= x+5=7+5=12

So, answer is a, 12