Dilations

Q.

The image formed by a plane mirror is always:

1. Real and erect

2. Virtual and erect

3. Real and inverted

4. Virtual and inverted

Q.

The sides of a triangle are 35 cm, 54 cm, and 61 cm respectively. Find the length of its longest altitude.

1. $16\sqrt{5}cm$

2. $10\sqrt{5}cm$

3. $24\sqrt{5}cm$

4. $28cm$

Q.

Explain the nature of the image formed by plane mirror.

Q. If a figure is dilated with a scale factor of 2.5, then choose the correct staements.

1. The dilation is enlarged.
2. The dilation is reduced.
3. The dilation is similar to the original.
4. The dilation is congruent with the original.

Q. This method of drawing enlarged or reduced similar figure is called_______.

1. Tessellation
2. Dilation
3. Enlargement
4. Reduction

Q.

When a rectangle is rotated, then it changes to a square.

1. True

2. False

Q. (a) Find the value of x in the below diagram given that, $\angle ACB$ = 25${}^o$, $\angle CBA$ = 15${}^o$ and CD is the height of C from the extended line segment BA:




(b) The lengths of two sides of a triangle are 13 cm and 16 cm. The third side should lie between 'a' cm and 'b' cm for the triangle to be formed. Find the value of a + b? [4 MARKS]

Q.

The blue figure is a dilation of the red figure. Identify the type of dilation and find the scale factor.

Q.

Which of the following are known as types of transformations?

1. Translation

2. Rotation

3. Reflection

4. Dilation

Q.

Which transformation causes the change in the distance between points of an object?

1. Translation

2. Rotation

3. Reflection

4. None of the above

Q.

Which of the following can be the length of the third side of a triangle whose two sides measure $18$ cm and $14$ cm?

1. $4cm$

2. $3cm$

3. $5cm$

4. $32cm$

Q. The method of drawing enlarged or reduced image is known as _______

1. Tessellation
2. Simulation
3. Illussion
4. Dilation

Q.

If all the sides of $△CAT$ are equal to corresponding sides of $△DOG,$ then $△DOG\cong △CAT.$

1. True

2. False

Q.

Given below are the measurements of some parts of two triangles. Examine whether the two triangles or not by using SAS congruence rule. If the triangles are congruent, write them in symbolic form.

$$\begin{gathered} △ABC△DEF \\ AB=7cm,BC=5cm,\angle B=50°DE=5cm,EF=7cm,\angle E=50° \end{gathered}$$

Q. Question 8 (ii)
In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
$\angle DBCisarightangle.$

Q. Can the following triangles exist? [3 MARKS]
(i) AB = 8 cm, BC = 6 cm, AC = 10cm
(ii) MN = 9 cm, NO = 5 cm, OM = 4 cm
(iii) $\angle A$ = ${175}^{\circ }$, $\angle B$ = $5^{\circ }$ and $\angle C$ = $0^{\circ }$

Q. integration of dx/x with limits b and a

Q. What is the scale factor for any two congruent figures?

1. 1
2. > 1
3. < 1
4. 0.5

Q. A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height. 1.5 m casts a shadow of 3m, then find how far she is away from the base of the pole.

Q. In $△ABC,\angle ABC=\angle DAC,AB=8cm,AC=4cm,AD=5cm$. Find $BC$ and $CD$.

Q.

Rahul can paint the house in 7 days and Mahesh can do it in 9 days. How long will they take, if both Rahul and Mahesh work together?

1. 

2. 

3. 

4. 

Q. In the given figure, $\Delta ABC\sim \Delta DEF$ and $\Delta DEF$ is the dilation of $\Delta ABC$. What is the scale factor?

1. 1
2. 2
3. 0.5
4. 4

Q. The method of drawing enlarged or reduced image is known as _______

1. Tessellation
2. Simulation
3. Dilation
4. Illussion

Q. A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate the length of M' N'. if MN= 8 cm.

1. 6.4 cm
2. 4.4 cm
3. 5.4 cm
4. none of the above

Q. If side BC of $△ABC$ is equal to side PQ of $△PQR$ , ∠B = ∠P and ∠C = ∠Q. Then, which of the given options would be correct?

1. AC = PR
2. AB = RP
3. BC = RQ
4. ∠C = ∠P

Q. Let $\Delta ABC\sim \Delta DEF$. If $ar\left(\Delta ABC\right)=100{cm}^2,ar\left(\Delta DEF\right)=196{cm}^2$ and $DE=7cm$, then find $AB$.

Q. If you want to draw an aeroplane on a small sheet of paper while looking at a real plane on the runway, which of the following concepts do you use?

1. Similarity
2. Not possible to draw
3. Congruency
4. Dilation

Q.

What is the main functions of translation?

1. Shriking of an image

2. Enlargement of an image

3. Rotation of an image

4. Sliding of an image

Q. If 'n' is scale factor to draw a dilation, then choose the correct options.

1. If n > 1, then dilation is enlarged than the original.
2. If 0 < n < 1, then dilation is reduced than the original.
3. If n = 1, then dilation is equal to the original.
4. If n > 1, then dilation is reduced than the original.

Q.

In the figure given below, PTU is a straight line. What is the value of 𝒙?

A) 70°
B) 100°
C) 45°
D) 50°