equation of straight line

Question

Find the Equation of sides of a right angled isosceles triangle having base x=0 and whose vertex is (-2,-3)

Answer 1

It helps to draw a graph. Plot the given point (-2,-3) and notice that it is the point where the right angle (90 degree angle) is, in order for both sides to be equal.

That means each side slopes at a 45 degree angle and -45 degree angle, (half of 90 degrees) 45 degree slope = a slope of 1, -45 degree slope = -1 slope. An isosceles triangle has 2 sides equal, and 2 angles equal. 90/2=45 degrees

Use the point slope formula for the two lines

y-(-3) = 1(x-(-2)) or y+3=x+2 or x-y=1

the other line has slope -1

y+3=-(x+2) or y+3=-x-2 or x+y=-5

Answer 2

Draw and label a diagram!

For two lines toe be perpendicular (making the right angle), the slopes must be negative reciprocals of each other.

If x = 0 is the equation of the base then (-2, -3) must be equidistant from x = 0 (this to make triangle isosceles)

Two equations are

y = x - 1

y = -x - 5