place each given figure in a coordinate plane. what are the coordinates of each vertex?

a) a right triangle
b) an isosceles triangle

a) There are an infinite number of possibilites, and we cannot draw graphs for you. One right triangle would have corners at (0,0), (0,10) and (5,0)

b) Have one corner at (0,10), and put two other corners at (a,0) and (-a,0). a can be any real number.

If in your problem you were given two triangles with specific side lengths, then the numbers you choose would have to agree with them.

To place each given figure in a coordinate plane and find the coordinates of each vertex, you should start by understanding the properties of each figure.

a) Right Triangle:
A right triangle has one 90-degree angle. You need at least three points to define a triangle. Let's say the right angle is at vertex A.

To find the coordinates of the vertices, you can choose any two points and then calculate the third point based on the properties of right angles and slopes.

For example, let's say we choose vertex A at (0,0) and vertex B at (3,0). Since it is a right triangle, you can choose the third vertex to be (0,4) or (4,0) based on whether the triangle is pointing upwards or sideways.

So, the coordinates of the vertices could be:
A (0,0)
B (3,0)
C (0,4) or (4,0)

b) Isosceles Triangle:
An isosceles triangle has two sides of equal length. Again, you need at least three points to define a triangle. Let's say the triangle is isosceles with the equal sides at vertices A and B.

To find the coordinates of the vertices, you can choose any two points for the equal sides and then find the third point based on the properties of isosceles triangles and slopes.

For example, let's say we choose vertex A at (0,0) and vertex B at (3,0). Now, the third vertex could be anywhere on the line segment defined by these two points. Let's say we choose vertex C at (3,4).

So, the coordinates of the vertices could be:
A (0,0)
B (3,0)
C (3,4)

Remember, these are just examples, and you can choose different coordinates for each vertex as long as they satisfy the properties of the respective triangles.