Question

Segment AB with endpoints at A(3, 2) and B(3, 16) is partitioned by point P according to the ratio of 2:5. Find the coordinate of point P.Options-(3, 4)(3, 12)(3, 14)(3, 6)

Answer 1

Option B

( ( 3 , 6 ) )

Answer 2

we have that

A(3,2) and B(3,16)

we know that

AP/AB=2/(2+5)

AP/AB=2/7 ----> equation 1

step 1

Find out the distance AB in the x-coordinate (ABx)

ABx=3-3=0

that means

the x-coordinate of point P is 3

step 2

Find out the distance AB in the y-coordinate

ABy=16-2=14

Find out the distance AP in the y-coordinate (APy)

Remember that

AP/AB=2/7 ---------> APy/ABy=2/7

APy=(2/7)(ABy)

APy=(2/7)(14)

APy=4

Find out the y-coordinate of point P (Py)

Py=Ay+APy

Py=2+4=6

therefore

The coordinates of point P are (3,6)