Show that point (5, 3) is equidistant from the points (1, 1) and (3,-1).
Answers
Answer:
The distance of point (5,3) from (1,1) = The distance of point (5,3) from (3,-1) = 2√5 units
Step-by-step explanation:
In co-ordinate geometry, The distance between any two points on a line is calculated by the formula
√(x₂ - x₁)² + (y₂ - y₁)²
Here x1, y1 are coordinates of first point and x2, y2 are coordinates of second point.
Now, we have to find the distance of point (5,3) from (1,1) and (3,-1)
The distance of point (5,3) from (1,1) is:
x₁ = 5, x₂ = 1, y₁ = 3, and y₂ = 1
√(1- 5)² + (1 - 3)² = √(-4)² + (-2)²
= √16 + 4 = √20 = 2√5 units
The distance of point (5,3) from (3,-1) is
x₁ = 5, x₂ = 3, y₁ = 3, and y₂ = -1
√(3- 5)² + (-1 - 3)² = √(-2)² + (-4)²
= √4 + 16 = √20 = 2√5 units
The distance of point (5,3) from (1,1) = The distance of point (5,3) from (3,-1) = 2√5 units
So, the point (5, 3) is equidistant from the points (1, 1) and (3,-1).