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Answer :
The woman's eyes are 1.70 m above the floor, and she stands 2.00 m in front of a vertical plane mirror. The bottom edge of the mirror is 0.45 m above the floor. The horizontal distance from the base of the wall to the nearest point on the floor reflected in the mirror is approximately 2.19 meters.
To solve this problem, we can use the concept of similar triangles. The triangle formed by the woman's eyes, the bottom edge of the mirror, and the point on the floor is similar to the triangle formed by the woman's eyes, the base of the wall, and the point on the floor that can be seen reflected in the mirror.
Let's denote the distance from the base of the wall to the point on the floor as x (in meters).
Using the given measurements:
- The height of the woman's eyes above the floor is 1.70 m.
- The height of the bottom edge of the mirror above the floor is 45 cm, which is equal to 0.45 m.
- The distance from the woman to the mirror is 2.00 m.
We can set up the following proportion:
x / 2.00 = (x + 1.70) / 0.45
Now, we can solve this proportion to find the value of x.
Cross-multiplying the equation gives:
0.45x = 2.00(x + 1.70)
0.45x = 2.00x + 3.40
0.45x - 2.00x = 3.40
-1.55x = 3.40
x = 3.40 / -1.55
x ≈ -2.19
Since we are dealing with a distance, x cannot be negative. Therefore, we take the absolute value of x, which gives us:
x ≈ 2.19 meters
So, the horizontal distance from the base of the wall to the nearest point on the floor that can be seen reflected in the mirror is approximately 2.19 meters.
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