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atiyawhite4488
20.09.2020 •
Mathematics
Sheena made a scale drawing of her classroom using a scale of 1 inch = 10 feet. One wall of the classroom in the drawing is 4 inches long. Which proportion can be used to find x, the length of the actual wall, in feet? * a. 1/10 = 4/x b. 1/4 = x/10 c. 4/12x = 1/10 d .12x/10 = 1/4
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Ответ:
On the graph, you can join lines PP', QQ' and RR' to confirm that they meet at the origin O(0,0), which is also the centre of dilation.
Part A
Next, you can compare the lengths OP' and OP using the distance formula, namely mOP'=sqrt(1^2+2^2)=sqrt(5), while mOP = sqrt(3^2+6^2) = sqrt(45) = sqrt(3^2 *5) = 3sqrt(5).
This demonstrate that the scale factor of dilation, equal to mOP'/mOP equals sqrt(5)/3sqrt(5)=1/3.
Try the same with OQ' and OQ, as well as OR' and OR. You should get the same factor of 1/3. If not, there is an error in some of the calculations.
Part B:
Points reflected about the y-axis goes through the transformation as follows:
Sy (x,y) -> (-x,y)
That means you only have to flip the sign of x-coordinate.
For example, P(3,-6) will have its reflection on P"(-3,-6), and so on.
Part C:
PQR and P"Q"R" are congruent because all simple reflections reflected about any line or point conserve the lengths and angles of shapes.