# How do you find the symmetric point of a line?

## How do you find the symmetric point of a line?

If a graph does not change when reflected over a line or rotated around a point, the graph is symmetric with respect to that line or point. The following graph is symmetric with respect to the x-axis (y = 0). Note that if (x, y) is a point on the graph, then (x, – y) is also a point on the graph.

What is symmetric about a line?

A line of symmetry is a line that cuts a shape exactly in half. This means that if you were to fold the shape along the line, both halves would match exactly. Equally, if you were to place a mirror along the line, the shape would remain unchanged.

### Which functions are symmetrical about the origin?

A function that is symmetrical with respect to the origin is called an odd function.

How do you determine if a graph is symmetric with respect to the origin?

A graph is said to be symmetric about the origin if whenever (a,b) is on the graph then so is (−a,−b) . Here is a sketch of a graph that is symmetric about the origin.

## Are circles symmetric with respect to the origin?

with respect to the origin. Solution: This circle relation has symmetry with respect to the y-axis, x-axis, and the origin. It also has reflectional symmetry over any line passing through the origin and rotational symmetry through any angle with the origin as a fixed point.

What is a symmetrical point?

Point Symmetry is when every part has a matching part. the same distance from the central point. but in the opposite direction. It looks the same when viewed from opposite directions (180° rotation). Also called Origin Symmetry, and is identical to “Rotational Symmetry of Order 2”.

### What is the another name of line of symmetry?

The line of symmetry is also called the mirror line or axis of symmetry.

What is symmetrical to the origin?

## Is a graph symmetric with respect to the origin?

The graph of an equation is symmetric with respect to the origin if replacing x with –x and y with –y yields an equivalent equation. A function is called even if it is symmetry with respect to the y-axis.

Which is the symmetric equation of a line?

From here, the symmetric equations of the line are: 0, 0, 0 0 0 0 ≠ ≠ ≠ − = − = − x y z x y z u u u u z z u y y u x x. 0 Ex 5. Convert the vector equation of the line L:r = 3)+( −1 2,0 ),t ∈R. r to the parametric and symmetric equations.

### How to find the parametric equations of a line?

Find the parametric equations of the line Lthat passes through the points A(0,−1,2) and B(1,−1,3) . Describe the line. tR z t y x t L x y z t L r t t R u AB A L ∈ ⎪ ⎩ ⎪ ⎨ ⎧ = + =− = ∴ = − + = − + ∈ = = − ∈ , 2 1 ( , , ) (0, 1,2) (1,0,1) : (0, 1,2) (1,0,1), (1,0,1); (0, 1,2) r The line is parallel to the xz-plane.

When does a graph have symmetry with respect to the origin?

A graph has symmetry with respect to the origin if, whenever (x, y) is on the graph, so is the point (-x, -y). 3. A graph has symmetry with respect to the x-axis if, whenever (x, y) is on the

## Which is parallel to the origin of the line?

d) passes through the origin and is parallel to the xz-plane r =t(a,0,b), t∈R r . At least one of aor bis not 0 . C Parametric Equations Let rewrite the vector equation of a line: r =r0 +tu, t∈R r r r as: (x,y,z) =(x0,y0,z0)+t(ux,uy,uz), t∈Rr The parametric equationsof a line in R3are: tR z z tu y y tu x x tu z y x 0 0 0 Ex 4.