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)

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1