I would like to know how to solve it or a detailed answer so i cn use it to answer the rest of my questions.

I thought the midpoint formula would work but it doesn't. It would work if 3*jp = pk

Let's try the distance formula.

Distance d between points j and k is sq root (16 + 64) = 4√5

Divide this distance by 5. Therefore the distance from point j to point p is (4/5)√5

The distance D is sq root (x + 2)^2 + (y - 5)^2 which must equal (4/5)√5

We can change this equation to one variable by using the equation of the line containing points j and k.

The equation is y = -2x + 1

So our distance equation becomes (x + 2)^2 + (-2x + 1 - 5)^2 = 16/5

x^2 + 4x + 4 + 4x^2 + 16x + 16 = 16/5

5x^2 + 20x + 20 = 16/5

x^2 + 4x + 4 = 16/25

(x + 2)^2 = 16/25

x + 2 = 4/5 we ignore the negative root because point p would not lie between j and k

x = (4/5) - 2

x is approx. -1.2

y is approx. 3.4

Let's try the distance formula.

Distance d between points j and k is sq root (16 + 64) = 4√5

Divide this distance by 5. Therefore the distance from point j to point p is (4/5)√5

The distance D is sq root (x + 2)^2 + (y - 5)^2 which must equal (4/5)√5

We can change this equation to one variable by using the equation of the line containing points j and k.

The equation is y = -2x + 1

So our distance equation becomes (x + 2)^2 + (-2x + 1 - 5)^2 = 16/5

x^2 + 4x + 4 + 4x^2 + 16x + 16 = 16/5

5x^2 + 20x + 20 = 16/5

x^2 + 4x + 4 = 16/25

(x + 2)^2 = 16/25

x + 2 = 4/5 we ignore the negative root because point p would not lie between j and k

x = (4/5) - 2

x is approx. -1.2

y is approx. 3.4

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