The vertices of a triangle are p(-8, 6), q(1, -3), and r(-6, -3). Name the vertices of R y=x( PQR)
(x,y)→(y,x)
The vertices of a triangle are P (-8, 6), Q (1, -3), and R (-6, -3). Name the vertices after a reflection over y = x.
To find the vertices of triangle PQR with R being the y=x line, we need to find the point where the line y=x intersects the line segment PQ.
The line equation y = x represents all the points where the y-coordinate is equal to the x-coordinate.
Given the vertices of triangle PQR:
P(-8, 6)
Q(1, -3)
R(-6, -3)
We need to find the intersection point between the line y = x and the line segment PQ.
First, let's find the equation of the line segment PQ.
The slope of the line segment PQ is (change in y / change in x):
m = (y2 - y1) / (x2 - x1)
= (-3 - 6) / (1 - (-8))
= (-9) / (9)
= -1
Using the point-slope form of a line, we have:
y - y1 = m(x - x1)
For point P(-8, 6):
y - 6 = -1(x - (-8))
y - 6 = -1(x + 8)
y - 6 = -x - 8
y = -x - 8 + 6
y = -x - 2
Now, we have two equations:
1) y = x (the line we're looking for)
2) y = -x - 2 (line segment PQ)
To find the intersection point, we can set the two equations equal to each other:
x = -x - 2
Simplifying:
2x = -2
x = -1
Substituting x = -1 into either equation, we get y = -1.
Therefore, the intersection point of the line y = x and the line segment PQ is (-1, -1).
So, the vertices of triangle PQR, with R being the y=x line, are:
P(-8, 6)
Q(1, -3)
R(-1, -1)
To find the vertex of R in the triangle PQR, where the equation is y = x, you need to determine which point of the triangle lies on the line y = x.
To do this, you can compare the x-coordinate and y-coordinate values of each point in the triangle. When the x-coordinate is equal to the y-coordinate, that point lies on the line y = x.
Let's check the coordinates of the given triangle vertices:
Point P: (-8, 6)
Point Q: (1, -3)
Point R: (-6, -3)
By comparing the x and y values, we can see that the point R(-6, -3) satisfies the condition y = x. Therefore, the vertex of R in triangle PQR is (-6, -3).
So, the vertices of triangle PQR are:
P(-8, 6)
Q(1, -3)
R(-6, -3)