Hello there. To solve this question, we'll need to remember some properties on distances between two points in the cartesian plane.
First, given two points (x0, y0) and (x1, y1), the distance d between these points can be found using the Pythagorean theorem:
Knowing that the square of the hypotenuse of a right triangle is equal to the sum of the square of its legs, we'll have:
d² = (x1 - x0)² + (y1 - y0)²
Taking the square root on both sides, as d is positive, we get:
d = sqrt((x1 - x0)² + (y1 - y0)²)
When one of the points is the origin of the cartesian plane, it all comes down to calculate the square root of the sum of the squares of the coordinates of a point.
Now, solving the question.
We want to find which house is nearest to the grocery store.
Using the distance formula and the coordinates of the points, we'll have:
House A (-6, 1)
dA = sqrt((-6)² + 1²)
dA = sqrt(36 + 1)
dA = sqrt(37)
Using a calculator, we find that dA is approximately equal to 6.08
House B (4, 3)
dB = sqrt(4² + 3²)
dB = sqrt(16 + 9)
dB = sqrt(25)
dB = 5
House C (2, -5)
dC = sqrt(2² + (-5)²)
dC = sqrt(4 + 25)
dC = sqrt(29)
Using a calculator, we find that dC is approximately equal to 5.38
With these results, we can easily see that the house that is nearest to the grocery store is the House B.