Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

5. Find the point P along the directed line segment from X(-3, 3) to Y(6,-3) that divides
the segment in a 2:1 ratio.

Sagot :

tehorsesnameisfriday
Consider point P(x,y) such that P, X and Y are collinear,

As vectors

XP = XO + OZ where O(0,0)
XP = OZ - OX
XP= (x,y) - (-3,3)
XP = (x+3, y-3)

Similarly,

PY = (6-x, -3-y)

But XP= 2^PY

[x+3, y-3] = [2(6-x), 2(-3-y)]

Given both vectors are equal, as they go in the same direction, Solve for x and y accordingly:

x+3 = 12 - 2x

x = 3

y-3 = -6-2y

y = -1

Therefore, P(3,-1)

The point P along the directed line segment from X(-3, 3) to Y(6,-3) that divides the segment in a 2:1 ratio is  (3, -1).

What is section formula?

In coordinate geometry, Section formula is used to find the ratio in which a line segment is divided by a point internally or externally. It is used to find out the centroid, incenter and ex centers of a triangle

Given

[tex](x_{1} ,y_{1})[/tex] = X(-3, 3)

[tex](x_{2},y_{2} )[/tex] = Y(6,-3)

m: n = 2:1

Section formula = [tex](\frac{mx_{2}+nx_{1} }{m+n},\frac{my_{2}+ny_{1} }{m+n} )[/tex]

P(a, b) = [tex](\frac{2(6)+1(-3)}{2+1} ,\frac{2(-3)+1(3)}{2+1} )[/tex]

P(a, b) = [tex](\frac{12-3}{3},\frac{-6+3}{3} )[/tex]

P(a, b) = [tex](\frac{9}{3} ,\frac{-3}{3} )[/tex]

P(a, b) = (3, -1)

The point P along the directed line segment from X(-3, 3) to Y(6,-3) that divides the segment in a 2:1 ratio is  (3, -1).

Find out more information about section formula here

brainly.com/question/10916187

#SPJ2

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.