Grace has a segment with endpoints F (4.9) and G (7, 2) that is divided by a point H such that FH and GH form a 1:3 ratio. She knows that the distance between the x coordinates is 3 units. Which of the following fractions will let her find the x coordinate for
point H?
O
4
19
4
1

f is the midpoint of

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

(−$11) ⋅ 12

deductions are negative and there are 12 months in a year