Question

On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4

Answer 1

Answer:

-2

Step-by-step explanation:

The coordinate of a point that divides a line AB in a ratio a:b from A($x_1,y_1$) to B($x_2,y_2$) is given by the formula:

$(x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )$

Given that a line JK, with  Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:

$x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2$

Answer 2

Line segments can be divided into equal or unequal ratios

The x coordinate of the segment is -2

The coordinates of points J and K are given as:

$J = (-6,-2)$

$K = (8,-9)$

The ratio is given as:

$m : n =2 : 5$

The x-coordinate is then calculated using:

$x = (\frac{m}{m + n }) (x_2 - x_1) + x_1$

So, we have:

$x = (\frac{2}{2 + 5 }) (8 - -6) -6$

$x = (\frac{2}{7}) (14) -6$

Expand

$x = (2) (2) -6$

Open bracket

$x = 4 -6$

Subtract 6 from 4

$x = -2$

Hence, the x coordinate of the segment is -2

Read more about line ratios at:.

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