We read your photo as:

Plot the given points on the Cartesian plane.

English

ScanSolve AI Answer

Graph of y = x

Use the left and right arrow keys to trace the curve, up and down to jump between key points, and plus and minus to zoom.

Key points of y = x
Pointxy
x-intercept00

Step-by-step solution

12 steps

Part a· 2 steps

On the Cartesian plane below, draw the quadrilateral PQRS with vertices P(4,6), Q(6,3), R(4,4), and S(2,3).

  1. Plot the given points on the Cartesian plane.

    P(4,6)
    Q(6,3)
    R(4,4)
    S(2,3)

  2. Connect the points in order to form the quadrilateral PQRS.

    (This step requires a physical drawing on the provided graph paper, which cannot be done here. The points are plotted as described.)

Part b· 3 steps

Draw P'Q'R'S' the image of PQRS under the transformation defined by the translation vector T=(−7−6)T = \begin{pmatrix} -7 \\ -6 \end{pmatrix}. Write down the coordinates of P'Q'R'S'.

  1. Apply the translation vector to each vertex of PQRS.

    For a point (x,y)(x, y) and a translation vector (ab)\begin{pmatrix} a \\ b \end{pmatrix}, the image is (x+a,y+b)(x+a, y+b).

    P'(x', y') = P(4,6) + (−7−6)\begin{pmatrix} -7 \\ -6 \end{pmatrix} = (4−7,6−6)(4-7, 6-6) = (−3,0)(-3, 0)
    Q'(x', y') = Q(6,3) + (−7−6)\begin{pmatrix} -7 \\ -6 \end{pmatrix} = (6−7,3−6)(6-7, 3-6) = (−1,−3)(-1, -3)
    R'(x', y') = R(4,4) + (−7−6)\begin{pmatrix} -7 \\ -6 \end{pmatrix} = (4−7,4−6)(4-7, 4-6) = (−3,−2)(-3, -2)
    S'(x', y') = S(2,3) + (−7−6)\begin{pmatrix} -7 \\ -6 \end{pmatrix} = (2−7,3−6)(2-7, 3-6) = (−5,−3)(-5, -3)

  2. Write down the coordinates of P'Q'R'S'.

    The coordinates are:
    P' = (−3,0)\boxed{(-3, 0)}
    Q' = (−1,−3)\boxed{(-1, -3)}
    R' = (−3,−2)\boxed{(-3, -2)}
    S' = (−5,−3)\boxed{(-5, -3)}

  3. Draw the image P'Q'R'S' on the same Cartesian plane.

    (This step requires a physical drawing on the provided graph paper, which cannot be done here. The points are plotted as described.)

Part c· 3 steps

P''Q''R''S'' is the image of P'Q'R'S' when reflected in the line y=1y=1. On the same plane, draw P''Q''R''S''.

  1. Apply the reflection in the line y=1y=1 to each vertex of P'Q'R'S'.

    For a reflection in the line y=ky=k, a point (x,y)(x, y) maps to (x,2k−y)(x, 2k-y). Here k=1k=1.
    So, (x,y)→(x,2(1)−y)=(x,2−y)(x, y) \to (x, 2(1)-y) = (x, 2-y).

    P'' = P'(-3, 0) →(−3,2−0)\to (-3, 2-0) = (−3,2)(-3, 2)
    Q'' = Q'(-1, -3) →(−1,2−(−3))\to (-1, 2-(-3)) = (−1,2+3)(-1, 2+3) = (−1,5)(-1, 5)
    R'' = R'(-3, -2) →(−3,2−(−2))\to (-3, 2-(-2)) = (−3,2+2)(-3, 2+2) = (−3,4)(-3, 4)
    S'' = S'(-5, -3) →(−5,2−(−3))\to (-5, 2-(-3)) = (−5,2+3)(-5, 2+3) = (−5,5)(-5, 5)

  2. Write down the coordinates of P''Q''R''S''.

    The coordinates are:
    P'' = (−3,2)\boxed{(-3, 2)}
    Q'' = (−1,5)\boxed{(-1, 5)}
    R'' = (−3,4)\boxed{(-3, 4)}
    S'' = (−5,5)\boxed{(-5, 5)}

  3. Draw the image P''Q''R''S'' on the same Cartesian plane.

    (This step requires a physical drawing on the provided graph paper, which cannot be done here. The points are plotted as described.)

Part d· 4 steps

Draw P'''Q'''R'''S''' the image P''Q''R''S'' when reflected in the line y−x=0y-x=0.

  1. Understand the reflection line.

    The line y−x=0y-x=0 is equivalent to y=xy=x.

  2. Apply the reflection in the line y=xy=x to each vertex of P''Q''R''S''.

    For a reflection in the line y=xy=x, a point (x,y)(x, y) maps to (y,x)(y, x).

    P''' = P''(-3, 2) →(2,−3)\to (2, -3)
    Q''' = Q''(-1, 5) →(5,−1)\to (5, -1)
    R''' = R''(-3, 4) →(4,−3)\to (4, -3)
    S''' = S''(-5, 5) →(5,−5)\to (5, -5)

  3. Write down the coordinates of P'''Q'''R'''S'''.

    The coordinates are:
    P''' = (2,−3)\boxed{(2, -3)}
    Q''' = (5,−1)\boxed{(5, -1)}
    R''' = (4,−3)\boxed{(4, -3)}
    S''' = (5,−5)\boxed{(5, -5)}

  4. Draw the image P'''Q'''R'''S''' on the same Cartesian plane.

    (This step requires a physical drawing on the provided graph paper, which cannot be done here. The points are plotted as described.)

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More English Questions

QPlot the given data points.QComplete the tables below by determining the values for each equation. Plot each point (x, y) on the…QDraw the following straight line graphs on a Cartesian Plane.QDraw a Cartesian plane with the x and y-axes containing values from −8 to 8. Plot the points below:QProblem 33: Plot (3,4) and (−2,5) on the Cartesian plane.
See all English questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp