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?

A:1/4
B:1/3
C:3/4
D:3/1

30 POINTS AND BRAINLIEST FOR BEST

                                                                                                                     Hello, Your answer will be A. 1/4        

Step-by-step explanation:

The coordinates of a point (x,y) that divides a segment with end points (a,b), (c,d) into two parts with ratio m/n are found using the fraction m / (n + m) and the formulae:

x = a + [m / (m + n)] × (c - a)

y = b + [m / (m + n) ] × (d - b)

For this case:

Point F (4,9)

Point G (7,2)

m = 1

n = 3

Fraction = 1 / (1 + 3) = 1 / 4

Hence, the coordinates of the point H are:

x = 4 + (1/4)×(7 - 4) = 4 + 3/4 = 4.75

y = 9 + (1/4)×(2 - 9) = 9 - 7/4 = 7.25

Have a Great Day!

the answer is a reflection across the line m

step-by-step explanation:

on edge

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36