38% 12:19 Mon 18 Jan
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6. In the diagram,
AB = x cm
BC = (x + 5) cm
CD= (2x - 1) cm
AD = 28 cm
D
B
a Show that 4x + 4 = 28
(2 marks)
b Solve 4x + 4 = 28
(2 marks)
c Work out the length of BD.
(2 marks)

The answer is below

Step-by-step explanation:

The line segment addition postulate states that for a line segment AC, another point B lies on AC if the below equation is satisfied:

AB + BC = BC

a) From the question, since point B and C lies on AD, then:

AD= AB + BC + CD

Substituting:

28 = (x) + (x + 5) + (2x - 1)

collecting like terms:

x + x + 2x + 5 - 1 = 28

Simplifying:

4x + 4 = 28

b) Simplifying the equation:

4x + 4 = 28

subtract 4 from both sides:

4x + 4 - 4 = 28 - 4

4x = 24

Divide through by 4:

4x / 4 = 24 / 4

x = 6

c) Also, BD = BC + CD

Hence:

BD = (x  + 5) + (2x - 1)

x + 2x + 5 - 1 = BD

3x + 4 = BD

substitute value of x:

3(6) + 4 = BD

18 + 4 = BD

BD = 22

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: