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!

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.