Question

7. The reflection of the point (4.-13) in the
line 5x + y +6 =O is
O (
(-1,-14)
O (0,0)
O (3, 4)
O (1,2)​

Answer 1

(-1,-14)

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As you can see in the picture ,our objective is to find P’ which is the reflection of P write line L

• First lets find a perpendicular line to L i.e PP’ passing through P as shown .

Slope of line L is -5

So slope of PP’ will be (1/5)

Line PP’ is (y+13 / x-4) = 1/5

PP’ is x - 5y = 69

• Now lets find the intersection of L and PP’ which is V in the picture

By solving we get V as ( 39/26 , -351/26 )

• Finally time to find out P’

Since V is the midpoint of P(4 , -13) and P’ .

(P’ + P)/2 = V

P’ = [ 2 (39/26) -4 , 2 (-351/26)+13 ]

P’ = [ 2 (39/26) -4 , 2 (-351/26)+13 ]= [ -1 , -14 ]

The reflection of (4 , -13) wrt 5x+y+6 = 0 is (-1 , -14).