In the rectangular coordinate system, the line y = -x is the

Question

In the rectangular coordinate system, the line y = -x is the perpendicular bisector of segment RS and the y-axis is the perpendicular bisector of segment ST. If the coordinates of point R are (-3, 1), what are the coordinates of point T ?

A. (-1,3)
B.(-1,-3)
C. (3,-1)
D. (1,3)
E. (3,1)

A. (-1,3)
B. (-1,-3)
C. (3,-1)
D. (1,3)
E. (3,1)

Bunuel · Answer

There are several ways to solve this one, but the easiest one would be just to draw the diagram. y=-x is the diagonal line through the origin with the negative slope. The coordinates of S would be (-1, 3) and the coordinates of T (1, 3).

shekar123 · Answer

In the rectangular coordinate system to the left, the line y = -x is the perpendicular bisector of segment RS and the y-axis is the perpendicular bisector of segment ST . If the coordinates of point R are (-3, 1), what are the coordinates of point T ?

A)1,3

B)2,2

C)3,3

D)3,3

E)1,1

Attachments

co-ord.JPG [ 8.46 KiB | Viewed 14162 times ]

A)1,3

B)2,2

C)3,3

D)3,3

E)1,1

jlgdr · Answer

Just my 2c here For the mirror of x= -y Just grab the R (-3,1) and do exactly what equation tells you to do That is x = -y. So -3 is now 'y' coordinate 3. Likewise, 1 = -1 for 'x' coordinate So we end up with (-1,3) y axis should be straightforward Always keep into consideration signs for each quadrant for sanity check I. ++ II. -+ III. +- IV. -+ Hope it helps Cheers! J

WilDThiNg · Answer

Please would you mind further elaborating why coordinates of S would be (-1, 3) - I am a little retard with coord geo.

Thanks

Bunuel · Answer

We get these points by drawing the diagram with line y = -x and point (-3, 1). By looking at it, you'd be able to eliminate the wrong answers and getting the right one. Similar questions to practice: in-the-xy-coordinate-plane-is-point-r-equidistant-from-143502.html in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html the-coordinates-of-points-a-and-c-are-0-3-and-127769.html the-line-represented-by-the-equation-y-4-2x-is-the-127770.html if-point-a-coordinates-are-7-3-point-b-coordinates-a-141972.html in-the-rectangular-coordinate-system-the-line-y-x-is-the-88473.html in-the-rectangular-coordinate-system-above-the-line-y-x-144774.html the-line-represented-by-the-equation-y-4-2x-is-the-perpendi-87573.html in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html Hope it helps.

WilDThiNg · Answer

Many thanks for such a prompt response!

Fdambro294 · Answer

Concept: when an Original Point is Reflected over a LINE:

(1) the Original Point and the new Reflected “Mirror Image” Point are EQUI-DISTANT from the Line

AND

(2) this “Mirror Line” over which the Original Point was Reflected is the Perpendicular Bisector of the Line Segment connecting the 2 Points

Concept 2: when a Point is Reflected over the Line given by the Equation: y = -(x)

Original Point (X , Y)

——> become Reflected “Mirror” Point (-Y , -X)

In other words, when you Reflect a Point over the Line: y = -(x)

The Coordinates get SWITCHED and NEGATED

Thus, Point R (-3 , 1) Reflected over the Line: y = -(x) ———> results in the Mirror Point S with Coordinates of (-1 , + 3)

If you join a Line connecting Point R and its Reflected Point S, you can see that Line: y = -(x) is the PERPENDICULAR Bisector of Line Segment RS

Proof:

(1st) Point R (-3 , 1)

(a) Plot the Point on Line: y = -(x) that has the SAME X Coordinate of -3

(-3 , 3) will be on Line y = -(x). Call this Point A.

The Vertical Distance from Point R to this Point A on Line y = -(x) is exactly 2 Units

(b)Plot the Point on Line: y = -(x) that has the SAME Y Coordinate of +1

(-1 , 1) will be the Point on Line y = -(x). Call this Point B.

The Horizontal Distance from Point R to this Point B on Line y = -(x) is exactly 2 Units

(2nd) Reflected Image Point S (-1 , 3)

Perform the same logical exercise and connect Point S to Points A and B on the Mirror Line of : y = -(x)

You will see that this is a 2 by 2 Square. And in Squares, the 2 Diagonals from Vertex R to Vertex S and From Vertex A to Vertex B are Perpendicular Bisectors

Summary: this means Line y = -(x) will be the Perpendicular Bisector of the Line Segment dawn from Point R (-3 , 1) to Point S (-1 , 3)

Thus, Point S has the coordinates of (-1 , 3)

Lastly, we need the Y-Axis (given by Line Equation: x = 0) to be the Perpendicular Bisector of the Line Segment ST, with unknown Coordinates for Point T.

Using similar logic, if we Reflect Point R over the Y-Axis (x = 0) we will get the Reflected Image Point T. Just like above, the Y- Axis will be the Perpendicular Bisector of Line Segment ST

concept 3: when we Reflect an Original Point (X , Y) over the Y-Axis:

Original Point (X , Y) becomes ——> Reflected Image Point (-X , Y)

In other words, we keep the SAME Y Coordinate and NEGATE the X Coordinate.

Thus, Point T will be at (+1 , 3)

If you plot both these Points, it is easy to see that the Y Axis is the Perpendicular Bisector of Line Segment ST.

Answer -D-

(1 , 3) are Coordinates of Point T

Posted from my mobile device

bumpbot · Answer

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In the rectangular coordinate system, the line y = -x is the

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