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The diagram shows a right-angled triangle.
Two of the vertices are at
(34,28) and
(20,0).
NOT TO SCALE
The midpoints of the sides of the triangle are
A,B and
C.
Find the coordinates of
A,B and
C.

{:[A=(],[B=(],[C=(]:}

The diagram shows a right-angled triangle. $\newline$ Two of the vertices are at $(34,28)$ and $(20,0)$ . $\newline$ NOT TO SCALE $\newline$ The midpoints of the sides of the triangle are $A, B$ and $C$ . $\newline$ Find the coordinates of $A, B$ and $C$ . $\newline$ $\begin{array}{l} A=( \\ B=( \\ C=( \end{array}$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. The diagram shows a right-angled triangle.

\newline

Two of the vertices are at

(34,28)

and

(20,0)

.

\newline

NOT TO SCALE

\newline

The midpoints of the sides of the triangle are

A, B

and

C

.

\newline

Find the coordinates of

A, B

and

C

.

\newline

\begin{array}{l} A=( \\ B=( \\ C=( \end{array}

Find Midpoint A: To find the midpoint $A$ , which is the midpoint of the hypotenuse, we need to average the $x$ -coordinates and $y$ -coordinates of the vertices $(34,28)$ and $(20,0)$ . $\newline$ $A = \left(\frac{34 + 20}{2}, \frac{28 + 0}{2}\right)$ $\newline$ $A = \left(\frac{54}{2}, \frac{28}{2}\right)$ $\newline$ $A = (27, 14)$
Find Midpoint B: To find the midpoint B, we need to find the midpoint between the vertex at $(34,28)$ and the right angle, which is at $(34,0)$ since the triangle is right-angled and aligned with the axes. $\newline$ $B = ((34 + 34) / 2, (28 + 0) / 2)$ $\newline$ $B = (68 / 2, 28 / 2)$ $\newline$ $B = (34, 14)$
Find Midpoint C: To find the midpoint C, we need to find the midpoint between the vertex at $(20,0)$ and the right angle, which is at $(34,0)$ . $\newline$ $C = \left(\frac{20 + 34}{2}, \frac{0 + 0}{2}\right)$ $\newline$ $C = \left(\frac{54}{2}, \frac{0}{2}\right)$ $\newline$ $C = (27, 0)$

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