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Chapter 14: Q5. (page 583)

Prove that the point D which is as far behind the mirror as the object A is in front of the mirror lies on BC鈫�. (Hint: Show that 鈭�CBE and 鈭�EBD are supplementary.)

Short Answer

Expert verified

The proof is shown in the below steps.

Step by step solution

01

Step 1. Given Information.

The given statement is that the condition can be proved by proving that 鈭�CBE and 鈭�EBD are supplementary.

02

Step 2. Proof.

The geometric diagram to proof the condition.

To show that the point D lies on BC鈫� i.e. 鈭�CBE+鈭�EBD=180掳

In triangle AOB and DOB

AO鈮�OD鈭�AOB鈮�鈭�DOBBO炉鈮�BO炉

triangleAOB鈮�triangleDOBsideanglesidehence,m鈭�ABO=m鈭�OBD

Since EO is a straight line

Hence,

m鈭�ABO=m鈭�CBEusethelawofreflectionm鈭�EBD+m鈭�OBD=180掳EOisastraightlinem鈭�EBD+m鈭�ABO=180掳m鈭�ABO=m鈭�OBDm鈭�EBD+m鈭�CBE=180掳m鈭�ABO=m鈭�CBE

Hence, 鈭�CBE and 鈭�EBD are supplementary.

03

Step 3. Conclusion.

The given condition is proved.

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Repeat Exercise 39 letting j be the horizontal line with equation y=6.

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  2. Show that the distance travelled by the ball equals the distance H.

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