contestada

Consider the line segment PQ with endpoints P(- 3, - 2) and Q(2, 3). Which point divides the line segment directed from P to Q in the ratio of 3:2?

Consider the line segment PQ with endpoints P 3 2 and Q2 3 Which point divides the line segment directed from P to Q in the ratio of 32 class=

Respuesta :

s1m1

Answer:

(0,1) point C

Step-by-step explanation:

the line segment PQ is divided into 5 parts ( 3parts +2 parts)

Is very important that you keep the direction correct from P to Q

The point C divides the PQ into 3:2 ratio

xero099

(0, 1) is the point that divides the line segment directed from P to Q in the ration of 3 : 2.

Vectorially speaking, we determine the the location of the point that divides the line segment in the ratio of [tex]a : b[/tex].

[tex]R(x,y) = P(x,y) + \frac{a}{a+b}\cdot [Q(x,y) - P(x,y)][/tex] (1)

Where:

  • [tex]P(x,y)[/tex], [tex]Q(x,y)[/tex] - Endpoints.
  • [tex]R(x,y)[/tex] - Resulting point.

If we know that [tex]P(x,y) = (-3, -2)[/tex], [tex]Q(x,y) = (2, 3)[/tex], [tex]a = 3[/tex] and [tex]b = 2[/tex], then the location of the resulting point:

[tex]R(x,y) = (-3, -2) + \frac{3}{5}\cdot [(2,3)-(-3,-2)][/tex]

[tex]R(x,y) = (-3,-2) +\frac{3}{5}\cdot (5, 5)[/tex]

[tex]R(x,y) = (-3, -2) + (3,3)[/tex]

[tex]R(x,y) = (0, 1)[/tex]

(0, 1) is the point that divides the line segment directed from P to Q in the ration of 3 : 2.

We kindly invite to check this question on line segments: https://brainly.com/question/23297288

Otras preguntas