Answer:
C. (-1,-2)
Step-by-step explanation:
Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.
Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)
So x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Substituting the values of the coordinates, we have
x = (mx₂ + nx₁)/(m + n)
3 = (1 × x₂ + 2 × 5)/(2 + 1)
3 = (x₂ + 10)/3
multiplying through by 3, we have
9 = x₂ + 10
x₂ = 9 - 10
x₂ = -1
y = (my₂ + ny₁)/(m + n)
10 = (1 × y₂ + 2 × 16)/(2 + 1)
10 = (x₂ + 32)/3
multiplying through by 3, we have
30 = y₂ + 32
y₂ = 30 - 32
y₂ = -2
So, the coordinates of B are (-1, -2)
General Idea:
When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.
Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.
In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.
P(x, y) becomes
. We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.
Applying the concept:
The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.
Conclusion:
The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),
In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.
Answer:
The one with arrows are the answers
->Line segment E B is bisected by Line segment D F .
->A is the midpoint of Line segment F C .
Line segment F C bisects Line segment D B.
->Line segment E B is a segment bisector.
->FA = One-halfFC.
Line segment D A is congruent to Line segment A B .
Step-by-step explanation:
I did it on edge and got it right