Final answer:
The Right-angled triangle is most helpful in finding the distance between two points on the coordinate plane, as it allows the use of the Pythagorean theorem.
Step-by-step explanation:
To find the distance between the points (-4, 3) and (1, -2) on the coordinate plane, the most helpful type of triangle to use would be a Right-angled triangle. This is because the distance between two points forms the hypotenuse of a right triangle, and the difference in their x-coordinates and y-coordinates form the two legs of this triangle. You can then apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is a2 + b2 = c2. To solve for c, which represents the distance between the two points, you would use the formula c = √(a2 + b2).
The differences in the x-coordinates (-4 and 1) and y-coordinates (3 and -2) are the lengths a and b of the two legs. Calculating these, we have:
a = 1 - (-4) = 5
b = -2 - 3 = -5
Substituting into the Pythagorean theorem gives us:
c = √(52 + (-5)2) = √(25 + 25) = √50