What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?

To solve this problem, we are given the formulas for our new x and y. To use this formula, we must first establish our points 1 and 2. Since the problem specifically directed the point E which partitions the line segment “from J to K”, therefore

point 1 = point J = (x1, y1)

point 2 = point K = (x2, y2)

The variables m and n indicates the portion of partition segment JE and EK that takes up from the original segment. Since the ratio is 1:4, then:

JE = m = 1

EK = n = 4

Therefore calculating for x and y using the given formulas:

x = [1 / (1 + 4)] (25 – (-15)) + (-15)

x = -7

y = [1 / (1 + 4)] (15 – (-5)) + (-5)

y = -1

Therefore the coordinates of point E is (-7, -1)

ardni313 ardni313 · Answer 2 · 2019-10-30T03:46:08+01:00

The x- and y- coordinates of point E (-7,-1)

Further explanation

In the coordinates of the two-dimensional plane (xy) there is a position vector.

Two dimensions because the coordinates are only x and y, three dimensions if the coordinates are x, y, and z.

If there is a point P then

You can write P as:

P = xi + yi

where i denotes the unit vector in the x and y directions

While the size of the vector:

[tex]\displaystyle P = \sqrt{x^2+y^2}[/tex]

and its direction

[tex]\displaystyle \theta=arc\:tan\:\frac{y}{x}[/tex]

If a point C divides the line segment AB by the ratio m: n, then the coordinates of point C can be formulated:

[tex]\displaystyle \vec{C}=\frac{m\vec{b}+n\vec{a}}{m+n}[/tex]

Coordinate x :

[tex]\displaystyle x=\frac{m.x_2+n.x_1}{m+n}[/tex]

Coordinate y :

[tex]\displaystyle y=\frac{m.y_2+n.y_1}{m+n}[/tex]

line segment from J to K into a ratio of 1:4, then m = 1 and n = 4

(x1,y1) from point J= (-15,-5)

(x2,y2) from point K= (25,15)

So coordinates of point E :

Coordinate x :

[tex]\displaystyle x=\frac{1.25+4.-15}{5}[/tex]

x = -7

Coordinate y :

[tex]\displaystyle y=\frac{1.15+4.-5}{5}[/tex]

y = -1

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Keywords: line segment, vector, two-dimensional coordinates , x,y, partitions