Question

Triangle JKL has vertices J (-3, 1), K (-3, -2), and L (1, -2). Rotate ΔJKL 900 counterclockwise about the vertex J and write the coordinates of point K after rotation.

Answer 1

Triangle JKL has vertices J (-3, 1), K (-3, -2), and L (1, -2). Rotate $\Delta$JKL $90{}^{\circ}$ counterclockwise about the vertex J and write the coordinates of point K after rotation.

Solution:

Move the origin to the point J(-3,1), then the coordinates of the point K (-3,-2) to be

$$x _ {K} ^ {\prime} = x _ {K} - x _ {J} = - 3 + 3 = 0$$ $$y _ {K} ^ {\prime} = y _ {K} - y _ {J} = - 2 - 1 = - 3$$ $$\mathrm {K} ^ {\prime} (0, - 3)$$

Rotate the triangle counterclockwise around the new origin

$$x _ {K} ^ {\prime \prime} = - y _ {K} ^ {\prime} = 3$$ $$y _ {K} ^ {\prime \prime} = x _ {K} ^ {\prime} = 0$$

Move the origin to its original location

$$x _ {K} ^ {*} = x _ {K} ^ {\prime \prime} + x _ {J} = 3 - 3 = 0$$ $$y _ {K} ^ {*} = y _ {K} ^ {\prime \prime} + y _ {J} = 0 + 1 = 1$$

Answer: $K^{*}(0,1)$