Is it a right triangle? and how to you find the points in the slope?

Plot the points on the graph paper. When you connect the 3 points, you have a triangle. You cannot be certain it is a right triangle until you find the slopes of AB and AC. If the slopes have negative reciprocals, the lines are perpendicular. If they are perpendicular, it is a right triangle.

Slope formula:
(y2-y1)/(x2-x1)

Slope AB:
(6-3)/(6-9)= 3/-3= -1

Slope AC:
(6-2)/(6-2)= 4/4= 1

The slopes are negative reciprocals, which means the two lines are perpendicular, angle CAB is a right angle and the triangle is a right triangle. I attached a quick drawing of the triangle.

Hope this helps! :)

the image of (6, 9) under a dilation is (4, 6). the scale factor is

b. 2/3

Main idea on left, details on right