Slope & Scale Factor Quiz

Answer explanation

To calculate the slope, use the formula: slope = (y2 - y1) / (x2 - x1). Substituting the given points (2, 3) and (5, 11), slope = (11 - 3) / (5 - 2) = 8 / 3. Therefore, the correct slope is 8/3.

A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. If this triangle is scaled by a factor of 2, what will be the length of the longest side in the new triangle?

• 10 cm

• 24 cm

• 26 cm

• 20 cm

Answer explanation

The longest side in the original triangle is 13 cm. When scaled by a factor of 2, the new longest side will be 13 cm * 2 = 26 cm. Therefore, the correct answer is 26 cm.

Given a polygon with sides of lengths 3 cm, 4 cm, and 5 cm, if the scale factor is 3, what is the length of the side that was originally 4 cm?

• 7 cm

• 12 cm

• 9 cm

• 15 cm

Answer explanation

To find the length of the side that was originally 4 cm, multiply the original length by the scale factor. 4 cm * 3 = 12 cm. Therefore, the length of the side that was originally 4 cm is 12 cm.

• Because the triangles are congruent.

• Because the ratio of the vertical change to the horizontal change is constant.

• Because the triangles have the same area.

• Because the triangles have the same perimeter.

Answer explanation

Because the ratio of the vertical change to the horizontal change is constant.

A rectangle has a length of 8 cm and a width of 5 cm. If the scale factor is 0.5, what are the dimensions of the new rectangle?

• 4 cm by 2.5 cm

• 16 cm by 10 cm

• 4 cm by 5 cm

• 8 cm by 2.5 cm

Answer explanation

To find the dimensions of the new rectangle, multiply the original dimensions by the scale factor. 8 cm * 0.5 = 4 cm and 5 cm * 0.5 = 2.5 cm. Therefore, the new rectangle is 4 cm by 2.5 cm.

Answer explanation

To find the slope, use the formula: slope = (y2 - y1) / (x2 - x1). Substituting the points (-1, -2) and (3, 6), we get (6 - (-2)) / (3 - (-1)) = 8 / 4 = 2. Therefore, the slope is 2.

A scale drawing of a park to the actual park has a scale factor of 100. If the length of the park in the drawing is 5 cm, what is the actual length of the park?

• 50 cm

• 500 cm

• 5 m

• 50 m

Answer explanation

Since the scale factor is 100, the actual length is 100 times the length in the drawing. Therefore, the actual length of the park is 5 cm * 100 = 500 cm.

• 3 cm

• 4 cm

• 5 cm

• 6 cm

Answer explanation

When scaled by a factor of 1/2, the shortest side becomes 3 cm (6 cm * 1/2). Therefore, the length of the shortest side in the new triangle is 3 cm.

• Because the triangles are similar and have proportional sides.

• Because the triangles are different and have different sides.

• Because the triangles are congruent and have equal sides.

• Because the triangles have the same angles.

Answer explanation

Because the triangles are similar and have proportional sides.

A scale drawing of a building to the actual building has a scale factor of 200. If the height of the building in the drawing is 3 cm, what is the actual height of the building?

• 60 cm

• 600 cm

• 6 m

• 60 m

Answer explanation

Since the scale factor is 200, the actual height is 200 times the height in the drawing. Therefore, the actual height of the building is 3 cm * 200 = 600 cm.