A-the perimeter of a triangle with vertices (0,4),(0,0),(3,0)

B-The points (-4,0),(4,0) and (0,3) are vertices of which triangle?WHY EXPLAIN?

Let’s name the points as A(0,4), O(0,0) and C(3,0).
The points can be plotted as:

Clearly AO = 4 units and OB = 3 units

Hence perimeter of triangle AOB = 4 + 3 + 5 = 12 units.


Let’s name the points as A(0,3), B(-4,0) and C(4,0) and plot them on a graph as below.

It can be observed that ABC is an isosceles triangle with AB = AC.
Justification of the above: Notice that O is the mid-point of BC as BO = OC = 4 units.
Also AO is perpendicular to the base BC (being the x-y axes).
We learned in the chapter ‘triangles’ that if median is also the altitude then the triangle is isosceles.
Hence triangle ABC is isosceles with AB = AC.

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