SOLUTION: find the equation of the right angled isosceles triangle whose vertex is (-2,-3) and whose base is x=0. Plz provide me the answer with detail?

Question 894451: find the equation of the right angled isosceles triangle whose vertex is (-2,-3) and whose base is x=0. Plz provide me the answer with detail?
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
The base is ON the line x=0; the base IS NOT x=0.

The vertex point is to the left of the y-axis, and the base is on the y axis. The triangle as you described is a right triangle of the 45-45-90 type. If you sketch this and have adequate intuition, you see two perpendicular lines containing (-2,-3). Another fact you should quickly find is that distance from (-2,-3) to the base is |2|, or 2.

You are looking for some algebra and coordinate geometry here in a more formal way, but my sketch on paper shows a segment on the y axis of length 4 units. This isosceles triangle is cut into two smaller such triangles sharing the 2-unit length side between them, distance from (-2,-3) to the y-axis.

Slopes of the two longer (hypotenuse) segments are 1, and -1.
y-intercepts are (0,-1) and (0,-5).

You can find the "equations" of the lines containing those sides any way you want. Just you can continue knowing the three vertices of (-2,-3); (0,-1); and (0, -5).

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