Rectangle reflections

Geometry Level 3

In a rectangle $ABCD$ a point $E$ is taken on $CD$ such that the reflection of $D$ from the line mirror $AE$ lies on $BC$

Given $AB=7 \text m$ , $BC=25 \text m$ find distance $DE$ .

The answer is 3.571.

2 solutions

Pradeep Ch
Jun 6, 2014

if image is F(7,k). with D being origin. ADF is isoceles triangle.. so, AF = 25. so, CF = k = $25 - √(25^{2} - 7^{2})$ = 1. and i found out, DE = 25*k/7 = 25/7 = 3.5714.

Good solution

Ronak Agarwal - 7 years ago

may i knw hw u found out 25*k/7

Shaikh Waz Noori - 7 years ago

that's simple.. the product of the two slopes is -1 (condition of perpendicularity). so, -25/x * k/7 = -1. so, x= 25*k/7..

Pradeep Ch - 7 years ago

how can u assume ADF is isosceles triangle.let us take the F as (7,k) and E as (a,0).now u form straight line equation of AE and find out the distance of point D and F from the st.line and its the perpendicular distance and both must be equal. if we do so we get (50a-ka)=175.solving we get a=5 and k=15.explain?

Prudhvi Gundala - 6 years, 4 months ago

Raghavendra Srinivas
Jul 17, 2014

The approximate answer is just is the distance from the mirror to the image in the mirror is same then the distance between you and your image is in such way that mirror is placed at midpoint.even if u turn in some angular position also.it is approx same so.AB= DC and e is midpoint so 7/2 = 3.5

The exact answer isn't 3.5. E isn't the midpoint of DC, especially for rectangles with a different width/length.

Calvin Lin Staff - 6 years, 2 months ago

The ans .is 25/7

Tarun B - 3 years, 8 months ago

Rectangle reflections

The answer is 3.571.

2 solutions

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