These twenty-four problems practice Common Core standards 8.G.A.2, 8.G.A.3 and 8.G.A.4. Move points and triangles with translations, reflections, rotations and dilations on the coordinate plane, then use scale factors to decide whether figures are similar.
The problems run from single points to word problems and two-step sequences. Work from easiest to hardest and compare your coordinates with the answer key.
Problem 1: Translate a point
Translate the point \(A(3, -2)\) 4 units right and 5 units up. Write the coordinates of the image.
Problem 2: Reflect over the x-axis
Reflect the point \(B(5, -3)\) across the \(x\)-axis. Write the image.
Problem 3: Reflect over the y-axis
Reflect the point \(C(-4, 6)\) across the \(y\)-axis. Write the image.
Problem 4: Rotate 90 degrees
Rotate the point \(D(2, 5)\) \(90^{\circ}\) counterclockwise about the origin. Write the image.
Problem 5: Rotate 180 degrees
Rotate the point \(E(-3, 4)\) \(180^{\circ}\) about the origin. Write the image.
Problem 6: Rotate 270 degrees
Rotate the point \(F(6, -1)\) \(270^{\circ}\) counterclockwise about the origin. Write the image.
Problem 7: Dilate a point
Dilate the point \(G(4, -6)\) about the origin with scale factor 3. Write the image.
Problem 8: Shrink a point
Dilate the point \(H(12, 8)\) about the origin with scale factor \(\frac{1}{4}\). Write the image.
Problem 9: Translate a triangle
Translate triangle \(ABC\) 4 units left and 2 units up. Write the coordinates of \(A^{\prime}\), \(B^{\prime}\) and \(C^{\prime}\).
Problem 10: Name the motion
Name the single rigid motion that maps triangle \(DEF\) onto triangle \(D^{\prime}E^{\prime}F^{\prime}\). Give the rule for \((x,y)\).
Problem 11: Reflect a triangle
Reflect triangle \(GHI\) across the \(x\)-axis. Write the coordinates of the image vertices.
Problem 12: Rotate a triangle
Rotate triangle \(JKL\) \(90^{\circ}\) counterclockwise about the origin. Write the coordinates of the image vertices.
Problem 13: Dilate a triangle
Dilate triangle \(MNO\) about the origin with scale factor \(\frac{1}{2}\). Write the coordinates of the image vertices.
Problem 14: Rigid motions keep size
In triangle \(ABC\), \(AB=6\text{ in}\) and \(\angle B=52^{\circ}\). The triangle is reflected across a line to form triangle \(A^{\prime}B^{\prime}C^{\prime}\). Find \(A^{\prime}B^{\prime}\) and \(\angle B^{\prime}\).
Problem 15: Dilation and lengths
A triangle has sides \(4\text{ in}\), \(7\text{ in}\) and \(9\text{ in}\), and an angle of \(38^{\circ}\). It is dilated with scale factor 3. Find the three new side lengths and the new angle measure.
Problem 16: Find the scale factor
A dilation about the origin sends \(A(2,3)\) to \(A^{\prime}(10,15)\). Find the scale factor, then find the image of \(B(-4,1)\).
Problem 17: A reducing dilation
A dilation about the origin sends \(P(-6,9)\) to \(P^{\prime}(-2,3)\). Find the scale factor, then find the image of \(Q(12,-3)\).
Problem 18: Two moves in a row
Triangle \(RST\) has vertices \(R(1,1)\), \(S(4,1)\), \(T(4,3)\). Reflect it across the \(x\)-axis, then translate the result 3 units left. Write the final vertices. Is the final triangle congruent to \(RST\)? Explain.
Problem 19: Similar rectangles
Are the two rectangles similar? If so, find the scale factor from the small rectangle to the large one.
Problem 20: Missing side of a triangle
The two triangles are similar. Find the scale factor and the length \(x\).
Problem 21: Enlarging a photo
Maya has a photo that is 4 inches wide and 6 inches tall. She enlarges it, keeping the same shape, so it is 10 inches wide. How tall is the enlarged photo? Name the scale factor.
Problem 22: Logo on a screen
A school-store logo is 3 inches wide and 2 inches tall on a flyer. Jamal shrinks and enlarges copies for other uses. On a banner the logo is 4.5 inches wide. Find the scale factor and the banner height. Then find the width of a sticker copy that is 1.5 inches tall.
Problem 23: Describe a sequence
Describe a sequence of a dilation about the origin and a translation that maps triangle \(ABC\) onto triangle \(DEF\). Are the triangles similar? Congruent?
Problem 24: Game character
Diego designs a game character as a triangle with vertices \((2,4)\), \((6,4)\), \((2,10)\). He enlarges it with a dilation about the origin with scale factor 1.5, then flips it across the \(y\)-axis so it faces left. Write the final vertices. How long is the horizontal side of the final triangle?
See every chapter on the Grade 8 math page.