Answer:
I have this question too
Step-by-step explanation:
All i know is that the ASA shows that even when they are rotated or translated due to rigid motions, they are still congruent because it shows that the angles and sides are equal.
Answer:
no solution
Step-by-step explanation:
Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)
We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>
The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>
Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>
The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).
The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24
Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.
Answer 1 3/5 × 40=64
Step-by-step explanation:
4×2/5=1 3/5 4×10=40
The coordinates of P are (9, -2).
Algebraically speaking, a translation is defined by the following expression:
(1)
Where:
- Original point.
- Translated point.
- Translation vector.
If we know that
and
, then the coordinates of the original point is:
![P(x,y) = P'(x,y) - T(x,y)](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20P%27%28x%2Cy%29%20-%20T%28x%2Cy%29)
![P(x,y) = (1,-2)-(-8,0)](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%281%2C-2%29-%28-8%2C0%29)
![P(x,y) = (9,-2)](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%289%2C-2%29)
The coordinates of P are (9, -2).
We kindly invite to see this question on translations: brainly.com/question/17485121