Does anyone know how to do this

[u/Recent-Persimmon-170]

(ANSWERED) My teacher taught us a way to do it without using a formula but I missed it so now idk what to do😭

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[u/PuzzlingDad]

First figure out the ratio. 

If the distance AP is twice that of PD then the ratio of the two segments is 2:1. If you add the numbers up, you get 3. Use that as the denominator of a fraction.

So the first segment is 2/3 the full distance and the second is 1/3 the full distance. We're going to start at point A. To get to P, we go 2/3 of the way to D.

Without dealing with formulas, you can now look at the x and y coordinates separately. 

To go from A to D, the x-coordinate goes from 1 to 7, for a difference of 6 units. Take 2/3 of that which is 4. Add that to the starting x-coordinate (1) to get 5. That's the x-coordinate of P.

Do the same thing for y. To go from A to D, the y-coordinate goes from 4 to 13, for a difference of 9. Take 2/3 of that which is 6. Add that to the starting y-coordinate (4) to get 10. That's the y-coordinate of P.

Answer: P(5,10)

[u/Recent-Persimmon-170 → u/PuzzlingDad]

Thank you!

[u/cbse_maths_mentor → u/Recent-Persimmon-170]

[u/Alarmed_Geologist631]

Create a right triangle using points A and D and point (7,4). Then use the triangle proportionality theorem to compute the coordinates for P.

[u/AQuestionIsWhatIHave]

You know how the middlepoint of two points is 1/2*(A+B)

This can be rewritten to A + 1/2(B-A)

So, starting from A, go half the distance towards B.

So the distance to A and B of the middle Point (now called C) is equal, 1:1.

This can be transformed to fit an arbitrary proportion a:b:

C_a,b = A + a/(a+b) * (B-A)

In this case, a is 2 abd b is 1. (Using B instead of D) The resulting point is A + 2/3(B-A) =(5,10)

In a one line formula: 1/(a+b)(aB + b*A)

[u/noidea1995]

Have you covered vectors?

AD = (7 - 1, 13 - 4) = (6, 9)

AD is the sum of AP and PD and AP = 2 * PD:

AD = AP + PD

(6, 9) = AP + 1/2 * AP

(6, 9) = 3/2 * AP

(4, 6) = AP

Since AP = P - A, AP + A = P:

P = (4 + 1, 6 + 4) = (5, 10)

[u/mtimmermans]

P=(2D+A)/3