Question

Find the reflection of point (4,-13) about the line 5x+y+6=0

Answer 1

Answer: the reflection point of (4,-13) over the given line is (-1,-14)

Step-by-step explanation:

Explantion in the attached file, please for clearing doubt.

Answer 2

Answer:

(-1,-14)

Step-by-step explanation:

The given equation of line, 5x+y+6=0

Let reflection of point (4,-13) is (a,b)

Let the mid point of (4,-13) and (a,b) is (h,k)

The point (h,k) lie on line, 5x+y+6=0

Therefore, 5h + k + 6 = 0    or   k = -5h - 6 -------- (1)

Mid-point formula:

$h=\dfrac{a+4}{2}$

$k=\dfrac{b-13}{2}$

Slope of (4,-13) and (a,b)

$m_1=\dfrac{b+13}{a-4}$

The slope of line, 5x+y+6=0

$m_2=-5$

The product of m₁m₂ = -1

$\dfrac{b+13}{a-4}=\dfrac{1}{5}$

5b + 65 = a - 4

a = 5b + 69

$\dfrac{b-13}{2}=-5\dfrac{5b + 69+4}{2}-6$

$b-13=-25b-365-12$

$26b=-364$

$b=-14$

$a=5(-14)+69$

$a=-1$

Hence, the reflection of a point is (-1,-14)