Negative Scale Factor

 Let us see about the negative scale factor. The negative scale factor is also a factor in which the area of the different geometric shapes get reduced or the objects gets inverted. The area of the different geometric objects is negative due to the negative scale factor.

            To find the reduced area of the different geometric objects, let us see few worked examples in negative scale factor.

An enlargement using a negative scale factor is similar to an enlargement using a positive scale factor, but this time the image is on the other side of the center of enlargement, and it is upside down.

If -2 is used as a scale factor, say by applying it to a 3-4-5 right triangle, it would have the effect of turning the triangle inside out (mirror image) and stretching it by a factor of 2. That would be the same as stretching to a 6-8-10 right triangle and turning it upside down on the table top

You have to go through the coordinates of the points you have for the shape and multiply them by the negative number.

e.g with -2, if you had a point on (1,1) you would plot the new point on (-2,-2).
 

Once you go through all the points in the shape, you will see the new shape will be twice the size and flipped about the x,y axis.

 

Relationship between Negative Scale Factor and Geometric Shapes of an Object

 

1. The geometric shapes are increased, if the scale factor is positive.

2. The geometric shapes are decrease, if the scale factor is negative.

3. The geometric shapes will remain same, if the scale factor is zero.

 

Model Problems for Negative Scale Factor

 

Model1 for Negative Scale Factor

Ex : Find the enlarged area of the rectangle if the scale factor is -2cm, whose original area is 10cm2.

Sol :       Area of the rectangle = 10cm2

              Scale factor = -2cm

              The scale factor is 8 cm, let us multiply both the length and breadth by 8,

                             Area of the rectangle = l * b

                                   Where, l= length of the rectangle

                                    And b= breadth of the rectangle.

            The area of the enlarged rectangle = -2(l* b)

                                                              =-2(l*b)

                                                              = -2(10)

                                                              = -20 cm2

          Therefore, the area of the enlarged rectangle is -20 cm2.

The result will be inverted enlarged rectangle.

 

Model2 for Negative Scale Factor

 

Ex : Find the area of the triangle, if the scale factor is -3cm and whose area is 10cm2.

Sol :     Area of the triangle = 10cm2

            Then, the scale factor = -3cm

         Area of the triangle = a2

The area of the triangle and the scale factor has to be multiplied,

The enlarged area of the triangle is given by,

Enlarge area of the triangle = -3 (a2)

                                            = -3(10)2

          Therefore, the area of the triangle after enlargement process= -300 cm2.

triangle

Practice Problems – Negative Scale Factor

 

Pro 1. Find the enlarged area of the rectangle if the scale factor is -4cm, whose original area is 20cm2. Answer: Enlarged area of the rectangle is -80cm2.

Pro 2.  Find the area of the square, if the scale factor is -3cm and whose area is 9cm2. Answer: Enlarged area of the square is -243cm2.