Question

The coordinates of the vertices of a triangle of a triangle are T(-1,-3),0(7,5), and P(7,-2). What is the length of the segment joining the midpoint of line segment OT and point P ?

Answer 1

To find the length of the segment joining the midpoint of OT and point P, compute the midpoint of OT and apply the distance formula with the coordinates of the midpoint and point P.

Step-by-step explanation:

The question asks for the length of the segment joining the midpoint of line segment OT and point P with given coordinates T(-1,-3), O(7,5), and P(7,-2). To find the midpoint of OT, we need to calculate the average of the x-coordinates and the y-coordinates of points O and T.

The midpoint M can be found using the formula M = ((x1 + x2)/2, (y1 + y2)/2), which gives M = ((7 - 1)/2, (5 - 3)/2) = (3, 1). Now that we have the coordinates of M (3, 1) and P (7, -2), we can use the distance formula to find the length of MP, which is √((x2 - x1)² + (y2 - y1)²). This calculation results in a length of √((7 - 3)² + (-2 - 1)²) = √(16 + 9) = √25 = 5 units.

Answer 2

To find the length of the segment joining the midpoint of line segment OT and point P, we can first find the coordinates of the midpoint O and then use the distance formula to calculate the distance between O and P.

Step-by-step explanation:

To find the length of the segment joining the midpoint of line segment OT and point P, we first need to find the coordinates of point O which is the midpoint of line segment OT.

The coordinates of T are (-1, -3) and the coordinates of O can be found by averaging the x-coordinates and y-coordinates of T and the origin (0,0). So, the coordinates of O are ((-1+0)/2, (-3+0)/2) = (-0.5, -1.5).

Next, we can calculate the distance between O and P using the distance formula d = √((x₂-x₁)² + (y₂-y₁²). The coordinates of O are (-0.5, -1.5) and the coordinates of P are (7, -2).

Substituting these values into the distance formula, we have d = √((7-(-0.5))² + (-2-(-1.5))²) = √(7.5² + 0.5²) = √(57 + 0.25) = √(57.25).