Item 10 The endpoints of the directed line segment AB are A(−1, 2) and B(7, 8). Find the coordinates of point P along AB¯¯¯¯¯¯¯¯ so that the ratio of AP to PB is 1 to 3.

The coordinates of point P along AB is (1,6.5)

Step-by-step explanation:

We shall use the internal division formula to split AB in the ratio 1 to 3

Mathematically, that would be;

(x,y) = (nx1 + mx2)/m + n , (ny2 + my1)/m + n

m = 1 , n = 3

(x1,y1)= (-1,2)

(x2,y2) = (7,8)

(x,y) = (3(-1) + 1(7)/1+3 , (3(8) + 1(2)/1+3

(x,y) = (-3 + 7)/4, (24 + 2)/4

(x,y) = 4/4 , 26/4

(x,y) = (1, 6.5)

step-by-step explanation:

d .tv

step-by-step explanation:

the side tv is included in both triangles.   this means it corresponds to itself in the transformation.

this is justified by using the reflexive property, which states that anything is congruent to itself.