Pregunta
- The mid points of sides
and
of triangle
are
and
respectively. Find the length of side QR.
Find the area of the triangle formed by the points,
and
Ask by Barker Curry. in India
Jan 30,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The length of side
is 20 units, and the area of the triangle formed by points
,
, and
is 47 square units.
Solución
Let’s solve each part of the problem step-by-step.
1. Finding the Length of Side
in Triangle
Given:
- Midpoint of
is . - Midpoint of
is .
Steps:
-
Let the Coordinates of Point
be . -
Find Coordinates of Points
and : -
Since
is the midpoint of : -
Since
is the midpoint of :
-
-
Determine the Distance
: - Coordinates of
: - Coordinates of
: - Distance formula:
Substituting the coordinates:
- Coordinates of
Answer:
The length of side is 20 units.
The length of side
2. Finding the Area of Triangle Formed by Points
,
, and
Using the Shoelace Formula:
Substituting the Given Points:
Answer:
The area of the triangle is 47 square units.
The area of the triangle is 47 square units.
Summary:
- Length of side
: 20 units - Area of triangle
: 47 square units
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Bonus Knowledge
To find the length of side
in triangle
, we utilize the midpoint formula. The coordinates of midpoints
and
give us the following equations based on the coordinates of points
:
We can solve these equations to find the coordinates of points
. Since
can be expressed as the straight-line distance between points
and
, we need to essentially derive these points (though the actual values are needed for the exact length).
However, let’s say we computed
and
; the length can ultimately be found using the distance formula,
.
For the area calculation of triangle
with points
,
, and
, we can use the formula:
Plugging in the values:
This simplifies to:
Calculating results in an area of 53. Thus, the side
length can be found with the earlier established coordinates and the area of triangle
is 53.
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