Hiba grew up in Great Britain, where she learned metric measurements. Now she lives in the U.S., and at the doctors office, she
2 answers:
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The scale factor of dilation from ABC to is 0.333.
Step-by-step explanation:
Step 1:
First, we plot the coordinates of both triangles.
The coordinates of the triangle are as follows;
= (2, 3),
= (2, 1), and
= (3, 1).
The coordinates of triangle ABC are;
A = (4, 9), B = (4, 3), and C = (7, 3).
Step 2;
Next, we need to find the distances between at least two coordinates for both triangles.
The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.
The distance of , the distance of
.
The distance of AB the distance of BC
Step 3;
To calculate the scale factor, we divide the measurement after scaling by the same measurement before scaling.
In this case, it is the length of the AB.
So The scale factor for AB =
The scale factor for BC =
4x + 2y = 8 (1)
8x + 4y = -4y (2)
A) Two lines are parallel if they have the same gradient
- putting both equations into the gradient- intercept form ( y = mx + c where m is the gradient)
(1) 4x + 2y = 8
2y = 8 - 4x
y = -2x + 4
(2) 8x + 4y = -4y
<span> </span>8x = -4y - 4y
y =
y = -x
<span>Thus the gradient of the two equations are different and as such the two lines are not parallel
</span>
B) When two lines are perpendicular, the product of their gradient is -1
p = (-2) * (-1)
p = 2
<span> ∴ the two lines are not perpendicular either.</span>
Thus these lines are SKEWED LINES
8x + 4y = -4y (2)
A) Two lines are parallel if they have the same gradient
- putting both equations into the gradient- intercept form ( y = mx + c where m is the gradient)
(1) 4x + 2y = 8
2y = 8 - 4x
y = -2x + 4
(2) 8x + 4y = -4y
<span> </span>8x = -4y - 4y
y =
y = -x
<span>Thus the gradient of the two equations are different and as such the two lines are not parallel
</span>
B) When two lines are perpendicular, the product of their gradient is -1
p = (-2) * (-1)
p = 2
<span> ∴ the two lines are not perpendicular either.</span>
Thus these lines are SKEWED LINES
Answer: Options A and C.
Step-by-step explanation:
The parent exponential function has the form:
This can be transformated as following:
When you multiply the function by a factor <em>a</em> ()<em> </em>and <em>a>0 </em>, then the function is vertically stretched.
When you add a number <em>k</em> to the parent function, the function is shifted up ()
The parent function given in the problem is:
To obtain the function , the parent function is multiplied by a factor 3 (which is greater than 0) and the number 5 is added.
Therefore, the graph is shifted up and vertically stretched.