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A line segment is graphed on the coordinate plane. What point divides this segment in the ratio 2:3 ?

A Line Segment Is Graphed On The Coordinate Plane What Point Divides This Segment In The Ratio 23 class=

Sagot :

we have the points

A (1,-2) and B(5,3)

Find out the point (x,y) that divide the segment AB in a ratio 2:3

that means

AX/XB=2/3

step 1

Find out the horizontal distance AB

ABx=5-1=4 units

Find out the vertical distance AB

ABy=3-(-2)=5 units

step 2

we have that

the horizontal distance between A and x is

AX/XB=2/3

AX=(2/3)XB -----> equation 1

AX+XB=4 -----> equation 2

substitute equation 1 in equation 2

(2/3)XB+XB=4

(5/3)XB=4

XB=12/5

XB=2.4

the x-coordinate of X is

x=5-2.4=2.6

Find out the y-cpoordinate

AX=(2/3)XB -----> equation 1

AX+XB=5 ------> equation 2

substitute equation 1 in equation 2

(2/3)XB+XB=5

5/3(XB)=5

XB=3

the y-coordinate of X is

y=3-3=0

answer is

the coordinate of the point is (2.6,0)

answer is option A

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