Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
In the given diagram, ∆ABC is a right triangle with . Segment AB is divided into four equal parts.

A right triangle A C B with A at (negative 3, negative 1), C at (negative 3, negative 3), and B at (6, negative 3). Side A B has 3 points D, E, and F, from the top to the bottom in equal increments. A line runs down from D to G on side C B.

The coordinates of point F are (
,
), and the coordinates of point G are (
,
).

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Martebi Martebi · Answer 1 · 2022-08-05T21:47:56+02:00

The coordinates of point F are (15/4 , -5/2)

From the image attached:

AB divided into 4 similar parts, hence

Note that the rule of the mid-point states that:

When M (x , y) is the mid-point of the segment of AB, where A (x1 , y1) and B (x2 , y2), Then x = (x1 + x2)/2 and that of y = (y1 + y2)/2

Then lets solve for points E, F, D

Since A (-3 , -1) and B (6 , -3),

E is the mid-point of AB

Then E =[(-3 + 6)/2, (-1 + -3)/2]

= (3/2 , -2)

Since F is the mid-point of EB,

E (3/2 , -2) , B (6 , -3)

Then F = [(3/2 + 6)/2 , (-2 + -3)/2]

= (15/4 , -5/2)

Since D is the mid-point of AE, A (-3 , -1), E (3/2 , -2)

Then D = [(-3 + 3/2)/2 , (-1 + -2)/2]

= (-3/4 , -3/2)

Note also that:

BC is said to be an horizontal segment due to the fact that B and C have similar y - coordinate and G can be found on BC.

Since the y-coordinate of G is similar to y-coordinate of B and C

Then y-coordinate of G is = -3

Since DG ⊥ BC

Then DG = vertical segment

So G has similar x-coordinate of D

Then The x-coordinate of G = -3/4

The G = (-3/4 , -3)

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